Question

In a game, a player flips a coin three times. If the coin shows heads, the player wins $ 1, and if it shows tails, the player loses $ 1. What is the expected value of the p

Answer 1

The expected value of the game is 0, which means that, on average, the player neither wins nor loses money in the long run.

Step-by-step explanation:

The expected value of a game can be calculated by multiplying each outcome by its probability and summing up the results. In this case, the player can win $1 if the coin shows heads and lose $1 if the coin shows tails. The probability of getting heads is 0.5, since it is a fair coin. The expected value of winning $1 is:

Expected value = (Probability of winning)(Amount won) = (0.5)(1) = 0.5

Similarly, the probability of losing $1 is also 0.5. The expected value of losing $1 is:

Expected value = (Probability of losing)(Amount lost) = (0.5)(-1) = -0.5

Adding these two expected values together, we get:

Expected value = 0.5 + (-0.5) = 0

This means that, on average, the player neither wins nor loses money in the long run when playing this game.