# Is it true that the chances of a person winning a lottery ticket increase if more tickets are bought?

justaguide | College Teacher | (Level 2) Distinguished Educator

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It is true that the chances of winning a lottery are increased if a larger number of tickets are bought.

This follows from the rule that the probability of one of n events taking place is the sum of their individual probabilities. For example if the probability of an event A is P(A) and that of an event B is P(B), the probability of either event A or event B taking place is P(A) + P(B).

In the case of a lottery ticket the probability of a ticket being the winning ticket is 1/N where N is the total number of tickets. If a person buys n tickets the probability of winning is increased to n*(1/N). As n increases so does the probability of winning the lottery. As a matter of fact if a person were to buy all the tickets in the lottery, winning the lottery is certain, though that would not be an appropriate thing to do as the cost of the tickets would exceed the prize money.

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