Question
Benjamin plays a game that costs him $10. If he wins, he will get $25. The probability of him winning is 40%. Based on the expected value, should Benjamin play the game?
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Answer to a math question Benjamin plays a game that costs him $10. If he wins, he will get $25. The probability of him winning is 40%. Based on the expected value, should Benjamin play the game?
Maude
4.7107 Answers
Step 1: Calculate Benjamin's expected value.
Let X be the random variable representing Benjamin's winnings.
The probability of winning is 40%, so the probability of losing is 60%.
Therefore, Benjamin's expected value can be calculated as follows:
E(X) = (\$25 \times 0.40) + (-\$10 \times 0.60)
E(X) = \$10 + (-\$6)
E(X) = \$4
Step 2: Analyze the expected value.
If Benjamin plays the game many times, on average, he can expect to win $4 each time he plays.
Step 3: Determine if Benjamin should play the game based on the expected value.
Since Benjamin's expected value is positive ($4), Benjamin should play the game because, on average, he can expect to make a profit.
Answer: Benjamin should play the game based on the expected value.
Let X be the random variable representing Benjamin's winnings.
The probability of winning is 40%, so the probability of losing is 60%.
Therefore, Benjamin's expected value can be calculated as follows:
Step 2: Analyze the expected value.
If Benjamin plays the game many times, on average, he can expect to win $4 each time he plays.
Step 3: Determine if Benjamin should play the game based on the expected value.
Since Benjamin's expected value is positive ($4), Benjamin should play the game because, on average, he can expect to make a profit.
Answer: Benjamin should play the game based on the expected value.
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