Using the same scenario as in number 2, your interviewer tells you that the game costs $1 to play and it has an expected value of 47 cents for every dollar spent. use the following payouts to determine

General
1

using the same scenario as in number 2, your interviewer tells you that the game costs $1 to play and it has an expected value of 47 cents for every dollar spent. use the following payouts to determine the expected value of the game. do you agree with your co-worker?s assertion? roll sum of 19 sum of 17 sum of 15 sum of 13 doubles other winnings $5 $3 $2 1 .5 $0

2

Does the game have a positive expected value?

Answer:
To determine the expected value of the game, we must calculate the average value of the payouts based on their probabilities. Given the payouts for each outcome, we first need to calculate the probabilities of each outcome occurring when rolling two dice.

There are 36 possible outcomes when rolling two dice (6 sides on the first die multiplied by 6 sides on the second die). Here are the probabilities and payouts for each outcome:

  • Rolling a sum of 19: There is only 1 way to get a sum of 19 (6, 6) out of 36 outcomes. Payout: $5
  • Rolling a sum of 17: There are 2 ways to get a sum of 17 (6, 1) and (1, 6) out of 36 outcomes. Payout: $3
  • Rolling a sum of 15: There are 4 ways to get a sum of 15 (6, 5), (5, 6), (6, 4), (4, 6) out of 36 outcomes. Payout: $2
  • Rolling a sum of 13: There are 6 ways to get a sum of 13 (6, 3), (3, 6), (6, 2), (2, 6), (5, 4), (4, 5) out of 36 outcomes. Payout: $1
  • Rolling doubles: There are 6 ways to roll doubles (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6) out of 36 outcomes. Payout: $0.5
  • Other outcomes (not mentioned): There are 15 ways to get other outcomes out of 36 outcomes. Payout: $0

Now, let’s calculate the expected value of the game:

Expected Value = (Payout 1 x Probability 1) + (Payout 2 x Probability 2) + … + (Payout n x Probability n)

Expected Value = ($5 x 1/36) + ($3 x 2/36) + ($2 x 4/36) + ($1 x 6/36) + ($0.5 x 6/36) + ($0 x 15/36)

Expected Value = ($5/36) + ($6/36) + ($8/36) + ($6/36) + ($3/36) + ($0)

Expected Value = $1.44

Since the game costs $1 to play and the expected value is $1.44, it means that for every $1 spent, the game is expected to return $1.44, which is a positive expected value. Therefore, I agree with my co-worker’s assertion that the game indeed has a positive expected value.