# Answer to Question #34766 in Statistics and Probability for Mohan Krishna

Question #34766

A frequently held lottery sells 100 tickets at $1 per ticket every time it is held. One of the tickets must be a winner. A player has $50 to spend. To maximize the probability of wining at least one lottery, should he buy 50 tickets in one lottery or one ticket in 50 lotteries?

Expert's answer

Let's find probabilities to win in both cases.

If the player buys 50 tickets in one lottery the probability to win equals to 50/100=1/2.

It the player buys 50 times one ticket probability to win equals to

P(win)=1-P(lose)=1-P(lose at every lottery)^50=1-(99/100)^50=0.395

So it is better to buy 50 tickets in one lottery.

If the player buys 50 tickets in one lottery the probability to win equals to 50/100=1/2.

It the player buys 50 times one ticket probability to win equals to

P(win)=1-P(lose)=1-P(lose at every lottery)^50=1-(99/100)^50=0.395

So it is better to buy 50 tickets in one lottery.

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