Which of the following games involving the roll of a single die is a fair bet?
A) Bet $1 and receive $1 if 3 or 4 comes up.
B) Bet $1 and receive $1 if 3, 4, or 5 comes up.
C) Bet $1 and receive $4 if 6 comes up.
D) None of the bets is a fair bet.

Question

Quizplus · Accepted Answer

A fair bet means that the expected value of the bet is zero. We can calculate the expected value of each bet as follows:
A) P(3 or 4) = 2/6, P(not 3 or 4) = 4/6, E = (1)(2/6) - (1)(4/6) = -1/3
B) P(3, 4, or 5) = 3/6, P(not 3, 4, or 5) = 3/6, E = (1)(3/6) - (1)(3/6) = 0
C) P(6) = 1/6, P(not 6) = 5/6, E = (4)(1/6) - (1)(5/6) = -1/6
Therefore, only option B has an expected value of zero, making it a fair bet.

Which of the Following Games Involving the Roll of a Single