Please help solving this Year 5 probability problem

srr on 27/12/2022 - 23:19

My boy got this problem in Year 5:

Ben and Jenny roll a dice once. The first one to roll a five wins. What are the probability of winning?

The teacher gave an answer 1/6 for both players. I mentioned that whoever starts first has an upper hand as the second player doesn't have a chance to roll at all.

I asked Chat GPT, and the AI was confused at first. However, after a few pointers came up with a good reasoning when Ben starts first:

In this game, the players take turns rolling a dice with 6 sides. The first player to roll a 5 wins.

There are 3 possible outcomes in this game: Ben winning, Jenny winning, or a draw.

The probability of Ben winning is 1/6 on his first roll.

The probability of Jenny winning is the probability that Ben does not roll a 5 on his first roll, which is 5/6, multiplied by the probability that Jenny rolls a 5 on her first roll, which is also 1/6. Therefore, the probability of Jenny winning is (5/6) * (1/6) = 5/36.

The probability of a draw is the probability that neither player wins, which is the probability that both players roll a number other than 5. This can be calculated as (5/6) * (5/6) = 25/36.

As a bonus, what are the probabilities of winning if Ben and Jenny keep rolling until someone wins?

Poll Options

  • 70
    1/6 and 5/36
  • 86
    1/6 and 1/6
  • 182
    the problem is too complex for Year 5
  • 7
    your answer
Education & Work

Comments

          • p1 ama on 28/12/2022 - 02:01
            +3

            @Kail:

            But it's a valid game rule, the players can choose to play the game this way.

            Yes, but the players will then not be competing against each other.

            For example, you could say that both Ben and Jenny are playing against the house. Whoever rolls a 5 will win. But that is a fundamentally different game is what I'm trying to say.

            • AnophthalmiaCervidae on 28/12/2022 - 13:58
              +3

              @p1 ama: Where does it say they are competing against each other and playing your game and not playing some other game against "the house"?
              If it is not the world championship of rolling 5 on a dice where there can only be one winner
              and they are playing (in rounds both rolling the dice at the same time) to win a prize that can be shared then both of them can potentially win at the same time and will each have a 1/6 chance of winning in the one roll.

              • p1 ama on 28/12/2022 - 19:31
                +1

                @AnophthalmiaCervidae: I interpreted it as implied in the question,

                Ben and Jenny roll a dice once. The first one to roll a five wins. What are the probability of winning?

                Since it says the first one to roll a 5, not whoever rolls a 5…etc.

                • AnophthalmiaCervidae on 29/12/2022 - 09:41
                  +3

                  @p1 ama: The first past the post wins a race but you can have a dead heat where two runners finish at the same time in which case they both win.

                  • p1 ama on 30/12/2022 - 15:02

                    @AnophthalmiaCervidae: Sure, if you want to interpret it that way. The fact that the question is so ambiguous and open to so many interpretations is the final conclusion that most of us got to in any case.

                    Ben and Jenny roll a dice once. The first one to roll a five wins. What are the probability of winning?

                    Even the first sentence, "Ben and Jenny roll a dice once", do they roll one each, or do they roll one together? If they roll one each, then do they roll at the same time (i.e. each roll then reveal the number), or is it a sequential roll, if it is a sequential roll, who goes first?

                    The issue is never that the probability is hard, but rather, that the question is unclear and cannot be mapped easily to what is physically happening when one plays the game.

    • blitz on 28/12/2022 - 01:55
      +2

      One of the best comments ever on OzBargain.

      • Jugganautx on 28/12/2022 - 05:16
        -1

        TLDR

        • p1 ama on 28/12/2022 - 13:43
          +3

          TLDR:

          1) If both players roll simultaneously, they each have a 5/36 chance of winning, with a 26/36 chance of a draw (1/36 being they both roll a 5, 25/36 being neither roll a 5).

          2) If one player rolls first, then whoever rolls first has a 1/6 chance of winning, the second roller has a 5/36 chance of winning, and there is a 25/36 chance of a draw. Essentially, the main difference is that the 1/36 chance of both rolling a 5 is "transferred" to the first roller compared to case (1).

          3) If it is an infinitely continuing game until one rolls a 5, then the first roller has a 6/11 chance of winning, and the second has a 5/11 chance of winning.

          • Quantumcat on 29/12/2022 - 22:24
            +1

            @p1 ama: I am impressed by your answers. So right, concise, well-written and easy to understand. Thank you.

    • rushil01 on 28/12/2022 - 02:47

      Nevermind, figured it out.

  • jaffar on 28/12/2022 - 00:49

    I couldn't figure it out but I found some answers that seem to be correct: (same as p1 ama above)
    https://math.stackexchange.com/questions/4389480/probability…
    https://math.stackexchange.com/questions/1973508/alternate-m…

  • Benoffie on 28/12/2022 - 01:06
    +14

    For the purposes of Year 5 math, the answer is 1/6.

    • Davo1111 on 28/12/2022 - 08:36
      +8

      This is the correct answer. Teacher probably sick of smartass parents over-thinking the question

      • Benoffie on 28/12/2022 - 10:49

        As a teacher this thread reminds me why i hate parent teacher interviews 😒

        • Scrooge McDuck on 28/12/2022 - 16:06

          As a competent adult, this thread reminds me of why I hate teachers.

        • Davo1111 on 28/12/2022 - 16:21

          In my job (mining), a lot of it is interpreting what the clients issue is, not what they think the issue is. (It's my equipment)

          As an example with OP. Probably asked "what is the answer?" … When the question is "why is 1/6 the answer?" (The answer is probably in the back of the book).

          If the teacher responded with "1/6, because both dice are thrown at the same time" - this would have solved this drama .

          It's really on OP to go into detail, but it does help to try and understand why they are asking the question.

          • srr on 29/12/2022 - 00:00

            @Davo1111:

            As an example with OP. Probably asked "what is the answer?" … When the question is "why is 1/6 the answer?" (The answer is probably in the back of the book).

            Actually this was not what happened. 6/36 and 5/36 answer was marked wrong, mentioning 1/6 the right one for both. During a meeting with the teacher I pointed out that the first to roll has to have the higher chance, proceeding with a table of 6x6 with outcomes and counting winning cases. The teacher agreed with my solution, to what I pointed that it's too complex for Year 5. The teacher said that the point of the exercise is to understand that the chance of rolling a 5 is 1/6, or something to that effect. I expressed regret that the wording of the problem is not correct. That was the end of the conversation.

        • p1 ama on 28/12/2022 - 19:34
          +2

          As a teacher, if you're not willing to be open-minded about being wrong and you don't enjoy being challenged, then you're unfit to be a teacher.

          If your reaction to being challenged isn't "oh, that's interesting, let's actually work through it", but rather "you're wrong, you're making my life hard, shut up", then you should not be teaching.

          This is coming from a teacher myself. One of the reasons I decided to leave the profession was closed-minded teachers who had a higher opinion of their own knowledge than they actually should have.

          One of my personal takeaways from teaching was what I learned from my students. It's sad that some teachers seem to learn nothing from their students at all.

          • Benoffie on 28/12/2022 - 22:03
            +2

            @p1 ama: Snore. This isnt learning from students. If it were it would mak for a fascinating conversation during class.

            No, this is from a parent, hyjacking an assignment out of context in an attempt to make themselves feel superior against Year 5 level curriculum content.

            And so, for that reason, i have a very low opinion. Like parents or community members who use logic like 'because i went to school, im qualified to comment'.

            I feel sorry for this teacher whose simple and Australian Curriculum meeting question on the fundamentals of past cannot predict future (in terms of Year 5 dice rolling), is being ripped a new one supposedly over the Xmas holidays.

            What I hate more, aside from not being paid atm to endure such nonsense during my 8 weeks unemployed stint, are self righteous teachers who think everything is 'a teachable moment' 🤣🤮

            • p1 ama on 29/12/2022 - 00:11
              +1

              @Benoffie:

              No, this is from a parent, hyjacking an assignment out of context in an attempt to make themselves feel superior against Year 5 level curriculum content.

              Not really - OP literally posted it on an online forum for discussion. You're making this sound like OP is outside of a classroom with a pitchfork ready to attack.

              And so, for that reason, i have a very low opinion. Like parents or community members who use logic like 'because i went to school, im qualified to comment'.

              Regardless of what OP's motives are or what your opinion of OP is, what is factual is factual. Being a teacher does not instantly make you correct or infallible.

              In my career of working with teachers in different capacities, I have seen countless examples of teachers being demonstrably incorrect, but not having the fortitude to be able to question their own understanding.

              I feel sorry for this teacher whose simple and Australian Curriculum meeting question on the fundamentals of past cannot predict future (in terms of Year 5 dice rolling), is being ripped a new one supposedly over the Xmas holidays.

              Again, where exactly has a teacher been "ripped a new one"? OP literally just made a forum post. Calm down.

              What I hate more, aside from not being paid atm to endure such nonsense during my 8 weeks unemployed stint, are self righteous teachers who think everything is 'a teachable moment' 🤣🤮

              I'm not of the belief that "everything is a teachable moment", but I am of the belief that teachers should be humble in their approach and be able to take feedback where it is received.

              If I was a approached by a parent, student, or another teacher saying what the OP said, you know what I would have said? Something along the lines of "Oh yeah, that does make sense, the question was worded a bit poorly hey? What I meant to say is [XYZ], I'll keep that in mind! Thanks!", it's not that hard is it?

              It's concerning that your view of any amount of (even valid) criticism is "ripping a new one". You're literally like the armies of dense teachers who were a dropkick in high school, barely passed uni, and scraped their way into teaching with just enough knowledge to pass the pre-requisite tests on a good day.

              I left the profession because of this sort of attitude, there's a statistic on something like 40% of teachers leaving in the first year and never coming back. At some point, you realise it's the system and the baked-in attitude that's the problem.

    • Hangryuman on 28/12/2022 - 12:45

      nah - ima go with 50:50 for anyone's chance of winning given an unnamed first player

      'Ben and Jenny roll a dice once. The first one to roll a five wins. What are the probability of winning?'

      the too-smart folk may jump for 1/6 but the question is NOT 'the probably of getting a 5 on any 1 roll of the dice'

      the question is the probability of winning - between 2 players - with effective equal chances - gotta be 50:50 or 1/2

      P.S. I hope the teacher didn't really write 'What are the probability of winning?'

  • sss333 on 28/12/2022 - 07:38
    +3

    Enjoy school holidays

  • Leiothrix on 28/12/2022 - 08:22
    +4

    "Ben and Jenny roll a dice once. The first one to roll a five wins. What are the probability of winning?"

    From your statement of the question they are rolling a dice at the same time. There is no mention of order, that is something that you assumed yourself.

    The key with any of these questions is both examination of the language used and divining the intention of the author when it is unclear.

    Writing down one's assumptions along with the answer would be the correct way of answering, but a lot of school teachers have fragile egos and wouldn't appreciate an apparent slight against them. So just write the most obvious answer.

    • trongy on 28/12/2022 - 12:50
      +2

      The first one to roll a five wins.

      The word first implies there is an order.

      However OP has admitted they don't remember the original wording, upholding the OzB forum tradition of prioritising disagreement over problem solving.

      • Davo1111 on 28/12/2022 - 16:26
        +2

        The word first implies there is an order.

        Not sure I agree with you. It's first past the post (rolling a 5).

        As an example, the drinking game flip cup. If you were to write rules, you'd mention "the first person to flip their cup wins". Both people are trying to flip their cup at the same time.

        upholding the OzB forum tradition of prioritising disagreement over problem solving.

        A thousand times this.

  • pegaxs on 28/12/2022 - 08:37

    If they both have their own die and the roll at the same time, they each have a 1:6.

    If they take turns, whoever goes first gets better odds, because the second player needs the first player to fail before they get their turn. 5:6 * 1:6.

    I'm probably wrong, because I'm the same person who even after having it explained over and over and for 20+ years, still have trouble getting my head around the Monty Hall paradox (And please, dont explain it to me, I have finally come to grips with it, I'm all good for explanations on it, Thanks.)

  • fishing on 28/12/2022 - 09:11
    +1

    A chance of :/2

    One or the other wins

    Read the question

    It doesn’t matter how many times you roll. There are two players and one will roll a 5 eventually

  • FlyingMiffy on 28/12/2022 - 09:35
    +1

    The question is probability for winning rather than the probability of a specific win for an individual so answer is 1/6 i.e. either winning is mutually exclusive. If you are asking specifically what is the probability of the second roller winning after the first fails, then its 5/36.

  • cheapskateteacher on 28/12/2022 - 10:13
    +1

    Actual Year 5 teacher here. No, this problem definitely isn’t too ‘complex’ for this year group. It is actually quite well targeted.

    • srr on 28/12/2022 - 10:14

      What’s the reasoning to get the right answer for 10-11 year olds?

      • Davo1111 on 28/12/2022 - 16:28

        Question doesn't make sense

      • Miss B on 28/12/2022 - 19:59
        +1

        I imagine they intended the question to be something like "Ben and Jenny roll a dice* once each. What is the probability of rolling a 5 for each of them?" I suspect they tried to jazz it up a bit to make it more interesting and unintentionally made it unclear.

        *I think a standard 6 sided dice can be assumed if it's not specified, though if they specified they can use other dice for other problems.

        The best way to understand what they are trying to ask with primary school maths questions, especially if they are poorly written, is to understand what they've been learning in class. They don't tend to throw kids curveballs on purpose, so they'll be doing the same thing they've been doing in class.

        • srr on 29/12/2022 - 00:16

          The best way to understand what they are trying to ask with primary school maths questions, especially if they are poorly written, is to understand what they've been learning in class.

          That's actually hard because there are no textbooks.

  • holdenmg on 28/12/2022 - 10:28
    +1

    The answer is 42.

  • ceroau on 28/12/2022 - 10:39
    +3

    You're over cooking it. The question is the probability of either Ben or Jenny rolling a 5. Which is 1/6, it is 1/6 up until the point one of them rolls but no where does it say one gets to roll first or that one has already rolled or that they get unlimited rolls etc. I'm far from a math expert I assume you're correct that once someone is elected to roll the probability splits for our two hypothetical individuals, and then the probability likely changes again for both once the first roll has occurred and so on and so far but the question wasn't asking any of that. It certainly wasn't asking you to work out who has the more chances of Win Ben or Jenny.

    It was a simple example you can infer from context (that context being it was a math problem for a year 5 student) that there was no additional or missing information so the problem wasn't written incorrectly. Sometimes Smart people who know how to solve very complex problems really struggle with solving simple ones because they're always looking for a bigger problem. This problem is simple. the dice has 6 faces with 6 numbers, one of those number is a five, therefore before you roll it there is a 1/6 chance of it landing on the 5.

    • srr on 28/12/2022 - 11:31

      The question is the probability of either Ben or Jenny rolling a 5

      This definitely wasn’t the question. Explanation why under no circumstances there’s a 1/6 chance of winning for both players described here:

      https://www.ozbargain.com.au/comment/13168980/redir

      • ceroau on 28/12/2022 - 23:30

        Now that dude is definitely over cooking it. Taking a simple problem and trying to come at it with an overly complex solution. At the end of the day we're all speculating without knowing how the question was written word for word. Do you know what it is? not roughly what it is but exactly because a single word can completely change the question.

        Either way the fact remains the teacher said the answer was 1/6 so it is 1/6 and it's going to stay 1/6 regardless of what's discussed what I guess I am curious about is whether the question is written wrong? or is your interpretation of the question wrong? .

  • mousie on 28/12/2022 - 10:41
    +2

    What is the probability that you want to be a year 5 teacher?

  • AnophthalmiaCervidae on 28/12/2022 - 10:43

    "Ben and Jenny roll a dice once"
    They each roll a die, it does not say they take turns in rolling.
    If they were taking turns and the Ben rolls a 5 and wins then Jenny would not get to roll.
    They both roll a dice once.
    So if they roll their dice at the same time the probability of Ben winning is 1/6 and the probability of Jenny winning is 1/6 (assuming you view a tie as both winning).
    The probability of someone winning on the single turn of rolling is (1-25/36) = 11/36.
    If they keep rolling until someone wins Ben and Jenny each have 6/11 chance of winning (it is better than 50:50 as one of the potential outcomes has both winning at the same time).

    • srr on 28/12/2022 - 11:36

      You’re close, but there’s an error 1/6+1/6 not equals to 11/36. Consider a case when both roll a 5, the probability of which is 1/36. This has to go somewhere - either to Ben or to Jenny, or both, or none of them. In any case it prevents 1/6 for at least one of them.

      • AnophthalmiaCervidae on 28/12/2022 - 12:21

        If you consider a tie as both winning then it is correct.
        There are 36 possible outcomes from rolling the two dice.
        5 of 36 will have Ben winning (and not Jenny)
        5 of 36 will have Jenny winning (and not Ben)
        1 of 36 will have both winning
        So 11/36 someone wins.

        1/6 + 1/6 - 1/36 = 11/36
        and
        5/36 + 1/36 = 1/6

        • srr on 28/12/2022 - 13:31

          If you consider a tie as both winning then it is correct.

          Discussed here https://www.ozbargain.com.au/comment/13169047/redir

          • AnophthalmiaCervidae on 29/12/2022 - 13:52

            @srr: and incorrectly concluded there.

            This is not possible within probability (i.e. both winning)… in this case, what you would have is the probability of Ben / Jenny winning being 1 / 6 each, with the probability of a draw being 25 / 36, which adds up to more than 1.

            If Ben winning and Jenny are not mutually exclusive they can both win (with a 1/36 probability)

            1/6 + 1/6 + 25/36 - 1/36 = 1

            • srr on 29/12/2022 - 14:11

              @AnophthalmiaCervidae: Are you saying that 5-5 case adds two outcomes and hence overall there are 37 points in the sample space of this game? I think you going to need a development of your own theory here. In the conventional probability theory this will be a separate outcome: 5/36 chance to win for Jenny and Ben, 1/36 to both winning, and 25/36 for draw.

              • AnophthalmiaCervidae on 29/12/2022 - 15:14

                @srr: The 5-5 case is one outcome under which both Ben and Jenny win. One outcome, two winners sharing the prize.

                5 outcomes will have Ben winning (and not Jenny)
                5 outcomes will have Jenny winning (and not Ben)
                1 outcome will have both winning
                25 outcomes neither win.

                Still 36 points in the sample space.

                6 have Ben winning
                6 have Jenny winning

                6/36 = 1/6

                1/36 is subtracted above because this is how often Ben and Jenny will both win in the same turn. Individual chance of winning (5/36+1/36 = 1/6) But you can not count the 1/36 twice as it is the same outcome.

  • StingyBritches on 28/12/2022 - 10:50
    +1

    42

    • holdenmg on 28/12/2022 - 11:14

      There was love for my saying 42 earlier either.

  • Beef Dingle Berry on 28/12/2022 - 11:14
    +3

    1/2.
    There is a 1/6 chance of rolling a 5 on the dice, but that wasn't the question. The question is what is the probability of winning, Ben and Jenny each have an equal chance of winning so it would be 1/2.

    • AnophthalmiaCervidae on 28/12/2022 - 11:26

      If you consider a tie as both Ben and Jenny winning and stop there then it is slightly better than half as you can have an outcome where they both roll a 5 on the same turn.
      If you have a tie-breaker and keep rolling until only one of them has a 5 then yes it would be 1/2.

    • trapper on 28/12/2022 - 12:11

      They only get one roll though, so the most likely outcome by far is that neither wins.

      • CommuterPolluter on 28/12/2022 - 13:16

        “Ben and Jenny roll a dice once. The first one to roll a five wins.“ The first sentence would indicate that your interpretation was a correct. The inclusion of ‘first’ in the second sentence implies either a) a first-mover advantage or b) multiple rounds. Neither of these are plausible. Poorly written questions like this used to shit me off as a student.

      • Beef Dingle Berry on 28/12/2022 - 13:54

        The question states 'The first one to roll a five wins' meaning mutiple rolls.

        • trapper on 04/01/2023 - 21:54

          No. The question explicitly says "Ben and Jenny roll a dice once".

    • belongsinforums on 28/12/2022 - 17:18

      This is the only correct answer, assuming there are two dice.

  • 2esc on 28/12/2022 - 11:31
    +3

    Its very common for my sons primary school teachers to not phrase a question correctly.

    We have even asked the teacher what does the question mean were we reading it wrong as we were taught differently many years ago. Teachers response was they didnt know what it meant either and they had to get back to us about it.

    If the teacher doesnt know what they are asking of a grade 4 student how is the kid supposed to have a chance a childs confidence is important.

    • Hangryuman on 28/12/2022 - 12:47

      'Its very common for my sons primary school teachers to not phrase a question correctly'

      I think the usual main question is 'can I has cheezburger ?'

    • Davo1111 on 28/12/2022 - 16:38

      Teachers response was they didnt know what it meant either and they had to get back to us about it.

      In their defence, I'd want to sit down and see the actual question, not take the parents verbal dictation as fact. (We already have that issue in this thread).

      Also, it's not really a priority. This is one parent question, in a bank of homework questions, in a class of students. The idea is for the child to understand a concept, not get 100%.

  • nobro25 on 28/12/2022 - 11:43

    I thinking you have to think in terms of soccer penalties when it's a draw at FT. Each team takes turns scoring penalties and they'll keep scoring unless one team misses.

  • jonkvh on 28/12/2022 - 11:46

    The question is asking only for 'one' and the 'initial' probability. Not every re-occurring event/probability afterwards.

    • srr on 28/12/2022 - 23:05
      +1

      Yes, that was a bonus question for curious.

  • trapper on 28/12/2022 - 12:16

    We don't have any information on who goes first (and it's not random either) so I think 1/6 to win is probably the best we can do.

  • Hangryuman on 28/12/2022 - 12:48
    +1

    wow - the number resiling to 1/6 here is impressive - given I believe that's the wrong answer - back to school boysengurls !

    • Davo1111 on 28/12/2022 - 16:49

      I think a poorly worded question and/or over-thinking parent has a pretty high probability.

      If you asked "what is a probability of rolling a 5 on a 6 sided dice?" Everyone would agree 1/6, but it was surrounded by a weirdly worded question

      • Hangryuman on 29/12/2022 - 16:51

        I'm thinking it was a trick question - where the too-quicks would jump at 1/6 !

        while the actual answer was so obvious most would walk straight past it

    • Diji on 29/12/2022 - 22:48

      the number resiling to 1/6 here is impressive
      Eh, I'm not a fan of Riesling.

  • Qazxswec on 28/12/2022 - 12:58

    if they only rolled the dice once each the answer is 1 in 6, but if they get to keep rolling the dice then eventually someone has to get it, meaning the winner has to be either ben or jerry, making it 50 50, but if they were both smart, they would stop this nonsense, team up and make a successful ice-cream company, and then they would both win

  • avoidfullprice on 28/12/2022 - 13:02

    As a bonus, what are the probabilities of winning if Ben and Jenny keep rolling until someone wins?

    Assume each roll is independent and has identical probability, the chance of winning is just 1/6 when it is your turn to roll.

    If it is Jenny’s turn, she has a 1/6 chance of winning.

    If it is Ben’s turn, Jenny has a 1/6 chance of losing, so 5/36 chance of winning on his turn.

    I mentioned that whoever starts first has an upper hand as the second player doesn't have a chance to roll at all.

    You can assume they will flip an unbiased coin and choose the starting player randomly. Afterwards the probability alternates on turns, so your upperhand concern becomes statistically irrelevant

  • chicguy on 28/12/2022 - 13:11
    +1

    Even if considering one go first, why would you need a university course or geometric series for this problem?

    On first roll:

    1st person: 1/6 chance to win = 6/36
    2nd person: 5/6 * 1/6 chance to win = 5/36

    So the ratio is 6/5 between 1st and 2nd persons on first roll.

    the draw chance of first roll (1 - 1st_person_win - 2nd_person_win) will be distributed with the same ratio on subsequence rolls, so it will always be 6/5 between 1st and 2nd persons.

    Conclusion: winning chance of 1st person is 6/11, and 2nd person is 5/11

  • crawfs on 28/12/2022 - 13:15
    +1

    I love poorly worded probability math questions, I remember arguing with a unit chair about something similar in university.

  • monkeyfood on 28/12/2022 - 13:26

    it says they roll a dice once, if they roll only once. First one to roll a 5… so basically they roll at the same time whichever dice stops first and happens to hit a 5 wins. Easy

    • srr on 28/12/2022 - 23:03

      Thank you, have you also worked out an answer?

  • larndis on 28/12/2022 - 13:41
    +3

    So, you want to argue the wording of the question but you haven't provided/don't know how it was worded? Seems like a pretty pointless exercise

    • srr on 28/12/2022 - 14:15

      Thank you for your opinion.

  • dwarves on 28/12/2022 - 13:56
    +2

    Dice is a plural. You mean die. They roll a die.

    • srr on 28/12/2022 - 14:12
      +1

      Thank you for your reply. I always eager to learn, but this time it looks like I won't be able to satisfy my eagerness. According to Macquarie Dictionary:

      1. …
      2. (construed as sing.) a single small cube of such a kind
        Usage: The singular form die is now rarely used. Dice is the usual for both the plural and the singular (def. 2)
      • dwarves on 28/12/2022 - 15:13
        +1

        Showin mah age 😥

      • belongsinforums on 29/12/2022 - 01:29

        Rarely? Maybe in America

  • Willy Beamish on 28/12/2022 - 14:41

    You asked the bot a different question.

    Ben and Jenny roll a dice once. The first one to roll a five wins. What are the probability of winning?

    If they have 2 dice and roll at the same time each then really who gives a shit.

    Get a hobby.

    • srr on 28/12/2022 - 14:49
      -1

      Get a hobby.

      Thank you for a life advice. That’s what ozbargain is for.

  • onelove on 28/12/2022 - 15:52

    It must be a homework from the Chinese Tuition Centre. :D :D

    • srr on 28/12/2022 - 23:00

      Nope, it was a QLD public school.

  • jackking on 28/12/2022 - 16:28
    +1

    Just assume both have a dice and roll simultaneously

    • srr on 29/12/2022 - 00:19

      What's the answer then?

  • fastnbulbous on 28/12/2022 - 16:59

    School in summertime?

    • srr on 29/12/2022 - 00:38

      No, the way this question ended up here was through ChatGPT. I was curious to see how the AI going to answer, and to my surprise it got 1/6 for both at first.

      I asked:

      it is a game of chance by rolling a dice with 6 sides. First to roll a 5 wins. Ben starts followed by Jenny. What are the chances to win for the players?

      and the bot replied:

      In this game, the players take turns rolling a dice with 6 sides. The first player to roll a 5 wins.

      If Ben goes first, he has a 1/6 chance of winning on his first roll. If he does not win on his first roll, then Jenny has a 1/6 chance of winning on her first roll. If neither player wins on their first roll, then Ben has another 1/6 chance of winning on his second roll, and so on.

      The same applies if Jenny goes first. She has a 1/6 chance of winning on her first roll. If she does not win on her first roll, then Ben has a 1/6 chance of winning on his first roll, and so on.

      Therefore, both players have an equal chance of winning, which is 1/6, or 16.667%.

      I hope this helps to clarify the solution to this problem. Please don't hesitate to ask if you have any further questions.

      I then had a nice chat with the bot, clarifying the problem and being amused with the answers. However in the end I was able to formulate the problem so it's not ambiguous to the bot and results in an answer I consider the right one. Then I thought it would be interesting to have a discussion here. One thing I can say for sure people are still better at chats than AI.

  • Davo1111 on 28/12/2022 - 17:12

    The issue is that OP is a boomer who had to share dice. Where the kid is a millennial and provided with (at least) 1 dice each.

    It's an assumption we didn't take into account when interpreting the question

    • srr on 29/12/2022 - 01:12

      Me:

      Davo1111 assumed that I am a boomer. Write an answer to Davo1111 in the Martin Luther King style assuring that I am not.

      Bot:

      Dear Davo1111,

      I understand that you have assumed that I am a boomer. I assure you that this assumption is incorrect. I am not a boomer, but rather a person of a different generation with my own unique experiences and perspectives.

      As Dr. Martin Luther King Jr. famously said, "We must learn to live together as brothers or perish together as fools." It is important that we do not make assumptions about one another based on stereotypes or superficial characteristics, but rather seek to understand and respect one another as individuals.

      I hope that you will consider this message and strive to approach others with an open mind and a willingness to see them as more than just a label or a stereotype.

      Sincerely,
      [Your name]

      I can sign this answer for sure as mine.

      • Davo1111 on 29/12/2022 - 01:23

        I don't respond to bots.

        Anyway, it's okay, I'm not having arguments with year 5 teachers over petty things

        • srr on 29/12/2022 - 08:11
          -1

          More context. I was taught in a different mathematical school. When my son comes for help with his homework, at times I don’t know the expected method to solve a problem. One that baffled me was “A carpenter made 71 legs for stools and chairs. Each stool has 3 legs while chair has 4. How many stools and how many chairs the carpenter made?” In my school of thought there’s always a class of problems and a method of solving them, where guessing is not used. Here I would solve it geometrically by building an ellipse Sx+Cy=N (S is the number of legs per stool, C per chair an N I’d the number of legs total), then adding a grid of natural numbers, finding all intersections of the grid with the ellipse. I was surprised that the expected method was to guess, which is actually a very good method to exercise multiplication and addition. I wish there were textbooks.

          • Plasticman on 30/12/2022 - 12:05

            @srr: Is that a trick question? It states that the carpenter made 71 legs for stools and chairs. One might conclude that the carpenter only made the legs and not the completed stools and chairs. Hence the answer should be zero.

            • srr on 31/12/2022 - 09:47

              @Plasticman: No it's not a trick question. The task is to find how many stool and how many chairs can be made out of 71 legs.

  • zeoko on 28/12/2022 - 17:18

    Could it be that both of them have a dice each and roll together?

    • Davo1111 on 28/12/2022 - 17:31

      (yes, we've collectively worked out the answer)

    • srr on 28/12/2022 - 23:11

      Could be. What’s the answer in this case?

      • zeoko on 29/12/2022 - 02:29

        Don't know. In not a probability expert like you. So please feel free to consider this case and let us know.

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