Lottery problem - dependent vs. independent events?

probability statistics

Solution 1:

Suppose the lottery sells $10,000,000$ tickets and draws two numbers as winners. The probability of any given ticket winning is then $\frac 1{5,000,000}$ but two tickets will win. The fallacy in your computation is assuming that the events of each ticket winning are independent. They are not. You are assuming they take each ticket and independently decide whether it wins. The probability of a winner is $1$. The probability that a given ticket will win is $\frac 1{5,000,000}$. You need to be careful with the question you are asking and the independence.

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