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

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

Using the same scenario as in question number 2, what is the expected value of the game based on the given payouts? Do you agree with LectureNotes’ assertion?

Answer:
To calculate the expected value of the game, we need to multiply each outcome by its respective probability and then sum up these values. Given the payouts and probabilities, we can calculate the expected value as follows:

[ EV = \Sigma (P(X_i) \times Payoff_i) ]

Where ( P(X_i) ) is the probability of outcome ( X_i ) and ( Payoff_i ) is the corresponding payoff.

Given Payouts and Probabilities:

  • Sum of 19: $5 (Probability: 1/36)
  • Sum of 17: $3 (Probability: 2/36)
  • Sum of 15: $2 (Probability: 3/36)
  • Sum of 13: $1 (Probability: 4/36)
  • Doubles: $0.5 (Probability: 6/36)
  • Other winnings: $0 (Probability: 20/36)

Now, let’s calculate the expected value:

[ EV = (1/36) * $5 + (2/36) * $3 + (3/36) * $2 + (4/36) * $1 + (6/36) * $0.5 + (20/36) * $0 ]

[ EV = $0.1388 + $0.1667 + $0.1667 + $0.1111 + $0.0833 + $0 ]

[ EV = $0.6666 ]

Therefore, the expected value of the game is $0.6666, which means that for every $1 spent, the player can expect to receive $0.6666 back on average. Since the expected value is less than $1, it indicates that the game is not favorable to the player, agreeing with LectureNotes’ assertion that the expected value is 47 cents for every dollar spent.