Question

In a game, you bet $2 and toss two coins. If two heads come up, you win a profit of 75 cents. If two tails come up, no one wins anything. Otherwise, you lose your wager. What is the expected value of this game?

Answer 1

The expected value of this game is -$0.50, meaning that on average, you would expect to lose 50 cents per game if you play it repeatedly. It is not recommended to play this game to win money.

Step-by-step explanation:

The expected value of this game can be calculated by multiplying the probability of each outcome by its corresponding value, and then summing them up. Let's calculate it step by step:

1. Probability of getting two heads: 1/4 (since there are 4 possible outcomes and only one of them is two heads)
2. Value of winning with two heads: $0.75
3. Probability of getting two tails: 1/4
4. Value of winning with two tails: $0
5. Probability of getting one head and one tail: 1/2 (since there are 2 possible outcomes)
6. Value of losing: -$2

Now, multiply each probability by its corresponding value and sum them up:

(1/4) * $0.75 + (1/4) * $0 + (1/2) * -$2 = -$0.50

Therefore, the expected value (expected net gain or loss) of this game is -$0.50. This means that on average, you would expect to lose 50 cents per game if you play it repeatedly. Considering this average loss, it is not recommended to play this game to win money.