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If there exists a fair National Lottery, that someone bets £1, Jackpot increases by £1, and there is p chance that he wins a Jackpot. If a Jackpot is won, it is reset to 0. repeats.

We can easily model this as a Bernoulli trials and the average Jackpot size is 1/p.

Now, if we observe that there are £M bets staked on the National Lottery, and it is won n times. What's the average Jackpot size in this case?

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