Question

You need to borrow money for gas, so you ask your mother and your sister. You can only borrow money from one of them. Before giving you money, they each say they will make you play a game. Your sister says she wants you to spin a spinner with six outcomes, numbered 1 through 6, on it. She will give you $5 times the number that the spinner lands on. Your mother says she wants you to spin a spinner with two outcomes, blue and red, on it. She will give you $5 if the spinner lands on blue and $25 if the spinner lands on red. Determine the expected value of each game and decide which offer you should take.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine the expected value of each game, we need to calculate the probability of each outcome and multiply it by the corresponding payout.

For the game with your sister:
- Probability of landing on 1, 2, 3, 4, 5, or 6 is each 1/6.
- Payout for landing on each number is $5 times that number.

Expected value for sister's game:
(1/6) * 5 + (1/6) * 10 + (1/6) * 15 + (1/6) * 20 + (1/6) * 25 + (1/6) * 30
= 5/6 * 5 + 10/6 * 5 + 15 /6 * 5 + 20/6 * 5 + 25/6 * 5 + 30/6 * 5
= 5/6 * 5 + 5/3 * 5 + 5/2 * 5 + 25/3 + 25/2 + 25
= 4.17 + 8.33 + 12.5 + 8.33 + 12.5 + 25
= $71.83

For the game with your mother:
- Probability of landing on blue is 1/2, and landing on red is 1/2.
- Payout for landing on blue is $5, and for landing on red is $25.

Expected value for mother's game:
(1/2) * 5 + (1/2) * 25
= 2.5 + 12.5
= $15

Therefore, you should take the offer from your sister with the spinner numbered 1 through 6, as it has a higher expected value of $71.83 compared to the expected value of $15 for your mother's game.