Question

Throw two dice. If the sum of the two dice is 7 or more, you win $38. If not, you pay me $48

Step 1 of 2: Find the expected value of the proposition. Round your answer to two decimal places. Losses must be expressed as negative values.

Step 2 of 2: If you played this game 685 times how much would you expect to win or lose? Round your answer to two decimal places. Losses must be entered as negative.

Answer 1

Step 1: The expected value of the proposition where one round is played is computed here as:

= 38*P(X >= 7) - 48*P( X < 7)

P(X < 7) can be obtained as:

• X = 2, in one way
• X = 3, in 2 ways: (2,1) and (1,2)
• X = 4, in 3 ways: (3,1), (2,2), and (1,3)

and so on...
P(X < 7) = (1 + 2 + 3 + 4 + 5)/36 = 5/12
P(X >= 7) = 1 - (5/12) = (7/12)

Therefore the expected value here is computed as:

= 38*(7/12) - 48*(5/12)

= 26/12 = 2.1667

Therefore 2.17 is the required expected value of the proposition if played once.

Step 2: Given that the game is played 685 times, the expected winning amount here is computed as:

= 685* Expected winning amount in each game

= 685*2.1667

= 1484.1667

Therefore $1,484.17 is the required expected winning amount here.