Solve the problem.
-Bob and Fred play the following game. Bob rolls a single die. If the result is the number 1, 2, 3, 4, Or 5 , Bob must pay Fred the number of dollars indicated by the number rolled. If a 6 is rolled, Fred must pay Bob $45. Find Fredʹs expectation.
A) $4.00
B) $0.00
C) -$10.00
D) -$5.00

Question

Quizplus · Accepted Answer

Fred's expectation can be calculated by taking the average of all possible outcomes. For rolls 1 through 5, Fred gains $1, $2, $3, $4, and $5 respectively, which sums to $15. For a roll of 6, Fred loses $45. The expectation is the sum of these outcomes divided by the number of outcomes: (1+2+3+4+5-45)/6 = -30/6 = -$5.

Solve the Problem. -Bob and Fred Play the Following Game. Bob Rolls a Bob