OOTS #1297 - The Discussion Thread

[Doug Lampert]

Which leads us back to the claim that the sample size is small. I'll assume that we're saying it's too small for the evidence to be overwhelming. It supremely isn't, despite our intuition saying so. You've got a better chance of winning the powerball by buying a single ticket twice in a row than getting 90 or more heads out of a 100 coin flips with a fair coin.

I believe this to be incorrect, the chance of winning powerball grand prize on a single ticket is 1 in 292.2 million [Per internet search], twice in a row is thus a chance of 1.17122E-17.

The chance of exactly 90 heads out of 100 tosses from EXCEL is "=(COMBIN(100,90)/2^100", which is 1.36554E-17. About 16% greater than the chance of two lottery wins in a row, and if you throw in the chance of 90 or more heads out of 100 is slightly larger still.

The two are however, surprisingly close.