There is a great Youtube Video documenting the process of a guy in England who set out to enter 1000 random competitions. He set a goal of entering 20 a day, for 50 days. The end result was 4 wins which is not a bad feat.
I guess the probability is fairly low if you just select 1000 random comps however looking at the wins on OzBargain and the AMA from multiple major comp winner maximum, there is a good chance of winning if you use the right strategies.
You can check how many comps you have entered & won by going to My Account-Lists-Competition. I've entered 948 comps with 20 wins..a lot better than Andrew did in the video. What's your win record?
News.com.au: Student enters 1000 competitions — did he win anything?
On OzB: 120 entered 4 wins (2 Coles).
Outside of here, when I was about 5 years old I won a jar of jelly beans for guessing how many were in there, was about 483 or something (long time ago).
More recently, I won a Nexus 7 (2013 model) in Nov 2013 as part of the Nestle Android Kit-Kat promo and have gotten great use out of it.