Question

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?

Answer 1

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.