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My maths problem involves probability relating to lotteries.

The odds of winning a lottery jackpot are 1 in 14 million. Over a period of time 50 million tickets have been bought, so the expected number of jackpot winners would be 3.5. However the actual number of jackpot winners is 7.

Is it possible to calculate a p value to prove that although the actual number of winners is higher than expected, it is still within normal expected ranges? Or are there any other statistical models that would answer the question?

I've seen worked examples for calculating the p value where all the outcomes are listed in excel, before applying the T test formula, however I'm not sure how to go about doing this when there are 50 million outcomes!

Thanks,

Paul