The expected value of playing the game is $2. This means that, on average, Jordan can expect to gain $2 for each game he plays.
The probability distribution given represents the possible outcomes for the number of shots Jordan makes in a randomly selected game, as well as the amount of money he gains from playing the game.
Let's analyze the probability distribution step-by-step:
1. If Jordan misses both shots, he gets nothing. This means that the probability of making zero shots is 60% (100% - 40%). In this case, he loses the $5 he paid to play the game.
2. If Jordan makes one shot, he gets his $5 back. The probability of making one shot is 40%. So, if he makes one shot, he breaks even and doesn't gain or lose any money.
3. If Jordan makes both shots, he gets $10 back. The probability of making both shots is also 40%. So, if he makes both shots, he gains $10 - $5 = $5.
To summarize the probability distribution:
- The probability of making zero shots is 60%, and the amount of money gained is $0.
- The probability of making one shot is 40%, and the amount of money gained is $0.
- The probability of making both shots is 40%, and the amount of money gained is $5.
This information allows us to calculate the expected value of playing the game. The expected value is found by multiplying each outcome by its probability and summing them up:
Expected Value = (Probability of making zero shots * Money gained from making zero shots) + (Probability of making one shot * Money gained from making one shot) + (Probability of making both shots * Money gained from making both shots)
Expected Value = (0.6 * $0) + (0.4 * $0) + (0.4 * $5) = $2