Questions: Expected Value Find the expected value of the winnings from a game that has the following payout probability distribution: Payout () 5 6 7 8 9 Probability 0.16 0.34 0.34 0.13 0.03 Expected Value =

Solution Steps

The payout values and their corresponding probabilities are given as:

• Payout (\$5) with probability \( 0.16 \)
• Payout (\$6) with probability \( 0.34 \)
• Payout (\$7) with probability \( 0.34 \)
• Payout (\$8) with probability \( 0.13 \)
• Payout (\$9) with probability \( 0.03 \)

Calculate the product of each payout and its corresponding probability:

• \( 5 \times 0.16 = 0.8 \)
• \( 6 \times 0.34 = 2.04 \)
• \( 7 \times 0.34 = 2.38 \)
• \( 8 \times 0.13 = 1.04 \)
• \( 9 \times 0.03 = 0.27 \)

Add all the products calculated in Step 2 to find the expected value: \[ \text{Expected Value} = 0.8 + 2.04 + 2.38 + 1.04 + 0.27 \]

\[ \text{Expected Value} = 6.53 \]

Final Answer