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There is a game where the outcome is a random integer from $1$ to $20$ . If the outcome is even, you win $\$15$ . If the outcome is odd, you win nothing. If you play the game, what is the expected payoff? $\newline$ $\$$ ____

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Expected values for a game of chance

Full solution

Q. There is a game where the outcome is a random integer from

1

to

20

. If the outcome is even, you win

\$15

. If the outcome is odd, you win nothing. If you play the game, what is the expected payoff?

\newline

\$

____

Calculate Probability of Winning: question_prompt: What is the expected payoff for playing the game where even numbers win $\$15$ and odd numbers win nothing? $\newline$ Step $1$ : Calculate the probability of winning. There are $10$ even numbers between $1$ and $20$ , so the probability of winning is $\frac{10}{20}$ or $\frac{1}{2}$ .
Calculate Expected Payoff: Step $2$ : Calculate the expected payoff. The expected payoff is the probability of winning multiplied by the amount won per win. So, Expected Payoff = $(\text{Probability of Winning}) \times (\text{Amount Won per Win})$ .
Plug in Values: Step $3$ : Plug in the values to calculate the expected payoff. Expected Payoff = $(\frac{1}{2}) \times \$15$ .
Find Expected Payoff: Step $4$ : Do the math to find the expected payoff. Expected Payoff = $\$7.50$ .

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