Question

question 18 · 1 point
jessie is playing craps and bets $5 on the come out roll. if a 7 or 11 is rolled, she wins $5. this happens with a probability of
$\frac{2}{9}$. if a 2, 3, or 12 is rolled, she loses her $5. this has a probability of $\frac{1}{9}$. if any other number is rolled, she does not win or
lose, and the game continues. find the expected value for jessie on the come out roll.

round to the nearest cent. do not round until the final calculation.

provide your answer below:

Explanation:

Step1: Recall Expected Value Formula

The expected value \( E(X) \) of a discrete random variable is given by \( E(X)=\sum x_iP(x_i) \), where \( x_i \) are the possible outcomes and \( P(x_i) \) are their corresponding probabilities.

Step2: Identify Outcomes and Probabilities

• Outcome 1: Wins \$5, probability \( P_1 = \frac{2}{9} \), so \( x_1 = 5 \).
• Outcome 2: Loses \$5 (or \( x_2=-5 \)), probability \( P_2=\frac{1}{9} \).
• Outcome 3: No win/lose, \( x_3 = 0 \), probability \( P_3=1 - \frac{2}{9}-\frac{1}{9}=\frac{6}{9}=\frac{2}{3} \).

Step3: Calculate Expected Value

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Answer:

\( \$0.56 \)