Question

Jessie is playing a game and bets $5 on the come out roll. If a 7 or 11 is rolled, she wins $5. This happens with a probability of 2/9. If a 2,3,or 12 is rolled, she loses her $5. This has a probability of 1/9. If any other number is rolled, she does not win or lose, and the game continues. Find the expected value for Jessie on the come out roll.

Answer 1

Answer: $5/9

Step-by-step explanation: 1. Winning with a 7 or 11:

- The probability of winning with a 7 or 11 is 2/9.

- If Jessie wins, she gets $5.

- So, the expected value for winning is (2/9) * $5 = $10/9.

2. Losing with a 2, 3, or 12:

- The probability of losing with a 2, 3, or 12 is 1/9.

- If Jessie loses, she loses $5.

- So, the expected value for losing is (1/9) * (-$5) = -$5/9.

3. Any other number rolled:

- The probability of any other number being rolled is 1 - (2/9 + 1/9) = 6/9.

- If Jessie doesn't win or lose, her balance remains unchanged, so the expected value is 0.

Now, we can sum up the expected values:

Expected value = (expected value for winning) + (expected value for losing) + (expected value for any other number rolled)

Expected value = $10/9 + (-$5/9) + 0

Expected value = $5/9

Therefore, the expected value for Jessie on the come out roll is $5/9. This means that on average, Jessie can expect to gain $5/9 on each come out roll in the long run.