Questions: Expected Value Find the expected value of the winnings from a game that has the following payout probability distribution: Payout () 0 1 3 9 27 Probability 0.67 0.22 0.07 0.03 0.01 Expected Value = ?

Expected Value

Find the expected value of the winnings from a game that has the following payout probability distribution:
Payout () 0 1 3 9 27
Probability 0.67 0.22 0.07 0.03 0.01

Expected Value = ?

Transcript text: Expected Value Find the expected value of the winnings from a game that has the following payout probability distribution: \begin{tabular}{c|ccccc} Payout (\$) & 0 & 1 & 3 & 9 & 27 \\ \hline Probability & 0.67 & 0.22 & 0.07 & 0.03 & 0.01 \end{tabular} Expected Value = $\square$ ?

Solution

Solution Steps

Step 1: Identify the Payouts and Probabilities

The payout values and their corresponding probabilities are given as:

Payouts: \( 0, 1, 3, 9, 27 \)
Probabilities: \( 0.67, 0.22, 0.07, 0.03, 0.01 \)

Step 2: Multiply Each Payout by Its Probability

Calculate the product of each payout and its corresponding probability:

\( 0 \times 0.67 = 0 \)
\( 1 \times 0.22 = 0.22 \)
\( 3 \times 0.07 = 0.21 \)
\( 9 \times 0.03 = 0.27 \)
\( 27 \times 0.01 = 0.27 \)

Step 3: Sum the Results

Add up all the products calculated in Step 2: \[ 0 + 0.22 + 0.21 + 0.27 + 0.27 = 0.97 \]

Final Answer

\(\boxed{0.97}\)

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