Question

There are 50 tickets in a raffle bag, and 10 of the tickets belong to Gary. A ticket is chosen at random, and the ticket owner's name is read. The ticket is mixed back into the bag. Another ticket is chosen, and the ticket owner's name is read.

What is the probability that Gary's name was read both times?
Write your answer as a percent.

Answer 1

The answer is 4%

Explanation:

In the prompt, it says that there are 50 tickets in a raffle bag, and 10 of those tickets belong to Gary. It then says that a ticket at random, is chosen, the owner's name is read, and the ticket is mixed back into the bag. And so there are still 10/50 tickets that belong to Gary and there are still a total of 50 tickets in the raffle bag (since it was replaced). The prompt then says that another ticket was is chosen and the ticket owner's name is read. The question is asking us what is the probability of Gary's name being read twice. Now a general probability rule is that for events A and B, where A occurs before B,

if there is a replacement, then

P(A and B) = P(A) • P(B). And so we'd take the original 10/50 tickets and multiply them by another 10/50 tickets, which equals 1/25, or 0.04. To convert this into a percent, you'd multiply 0.04 by 100 to get 4% our final answer.

Answer 2

I believe the answer is about 20%.