The number of jackpot winning lottery tickets given the number of tickets bought

Every lottery ticket bought has a probability of 1 in 13,000,000 of winning the jackpot. There is a standard method  (the Binomial distribution) for calculating the probability distribution of the number of winning tickets (you can experiment yourself by running this model in AgenaRisk). If we do not know the number of tickets bought then distribution for number of  wining tickets looks like this (we are assuming that the number of tickets boughts is Normally distributed with a mean around 20,000,000 and a wide variance).


So there is 0.26 probability of 0 winners and a slightly higher probability of 1 winner. The probability of  5 winners is about 0.03.

If we enter specific numbers of  tickets bought, as in the following examples, you can see how the probability distribution for number of winners changes.

lottery2 lotter3 lottery4
5,000,000 tickets bought 20,000,000 tickets bought 75,000,000 tickets bought

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Norman Fenton