Pedro has two options: he can enter raffle number 1, OR raffle number 2 along with raffle number 3. If Pedro chooses to enter raffle number 1, he can buy up to 100 raffle tickets. Each ticket has a 1 in 50 chance of getting selected. If Pedro chooses raffle number 2/raffle number 3, he will have a 1 in 10 chance for raffle 2, and a 1 in 20 chance for raffle 3. However, if Pedro chooses to enter raffle number 2/raffle number 3, he can only buy one ticket for raffle number 2, and one ticket for raffle number 3. Which option should Pedro choose--buying 100 tickets for raffle one, or buying one ticket for both raffle two and raffle 3?
To determine which option Pedro should choose, we need to calculate the expected value for each option. The expected value is the average outcome weighted by the probability of each outcome occurring.
For Option 1 (raffle number 1), let's calculate the expected value.
The probability of winning with one ticket is 1/50. So the expected value for one ticket is (1/50) * $0 (assuming no prize value).
Since Pedro can buy up to 100 tickets, we multiply the expected value of one ticket by the number of tickets: (1/50) * $0 * 100 = $0.
Therefore, the expected value for Option 1 is $0.
Now let's calculate the expected value for Option 2 (raffle number 2/raffle number 3).
For raffle number 2, the probability of winning is 1/10. Since Pedro can only buy one ticket, the expected value for raffle number 2 is (1/10) * $0 = $0.
For raffle number 3, the probability of winning is 1/20. Again, Pedro can only buy one ticket, so the expected value for raffle number 3 is (1/20) * $0 = $0.
Since Pedro participates in both raffle number 2 and raffle number 3, we sum up the expected values: $0 + $0 = $0.
Therefore, the expected value for Option 2 is also $0.
Considering the expected values for both options, Pedro should choose the option that is more convenient for him. In this case, since the expected values for both options are the same ($0), Pedro can choose either option based on his personal preference.