A gamble in which you win D dollars if the coin comes up heads, but lose D dollars if the coin comes up tails has an expected value of
A) 1/2D.
B) -1/2D.
C) D.
D) 0.

Question

Quizplus · Accepted Answer

The expected value of a gamble is found by taking the sum of the products of each possible outcome and its probability. In this case, there is a 1/2 probability of the coin coming up heads (resulting in a win of D dollars) and a 1/2 probability of the coin coming up tails (resulting in a loss of D dollars). So, the expected value is:

(1/2)(D) + (1/2)(-D) = 0

Therefore, the expected value of this gamble is 0. This means that, on average, you will neither win nor lose money in the long run by playing this game. Therefore, it is not a good choice to gamble.

A Gamble in Which You Win D Dollars If the Coin