Consider the following game. You roll a six-sided die and each time you roll a 6, you get $30. For all other outcomes you pay $6. Since the expected value of this game is $0, the game is called a(n)
A) gamble.
B) fair bet.
C) even game.
D) zero sum game.

Question

Quizplus · Accepted Answer

A fair bet is defined as a bet where the expected value of the outcomes is zero, meaning that over time, you neither gain nor lose money on average. In this game, the probability of rolling a 6 is 1/6, so the expected earnings are $30*(1/6) = $5. The probability of rolling any other number is 5/6, so the expected loss is $6*(5/6) = $5. Since the expected earnings equal the expected loss, the expected value of the game is $0, making it a fair bet.

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