Final answer:
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.