RonO (rono_60103) wrote,

Really Tiny Numbers

A discussion on an e-mail list this morning led me to spend some time calculating the probability of winning the powerball lottery. Actually, I cheated and let them calculate the odds for me, and then turned them into a probability.

They report the odds of winning as "1 in 146,107,962.00" which comes out to a probability of winning of 6.8443*10^-9 (or 6.8443e-09 on my pseudo calculator display). Now, obviously this is a small number, but it wasn't obvious how small until I went to calculate the odds of not winning the grand prize. When I tired it on the same pseudo calculator (WRPN version 1.0), I got a result of 1.0000. So I tried on bc on the sun I was logged into, and got 1. Finally I tried excel, and also got 1. This number is so small that the probability of not winning was equal to 1 after rounding on everything I tried.

I was, however, successful in calculating the expected winnings on a $1.00 ticket as $0.64 -- which is still a loss. I didn't take into account the possibility of multiple winners, and just now realized that i forgot to even try to take into account the odds of winning a lesser prize. I'll just leave that as an exercise for the students.


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