Questions: Find the expected value of the winnings from a game that has the following payout probability distribution: Payout () -6 -4 -2 0 2 Probability 0.34 0.13 0.06 0.13 0.34 Expected Value = Round to the nearest hundredth.

Find the expected value of the winnings from a game that has the following payout probability distribution:
Payout ()  -6  -4  -2  0  2 
Probability  0.34  0.13  0.06  0.13  0.34

Expected Value = 
Round to the nearest hundredth.
Transcript text: Find the expected value of the winnings from a game that has the following payout probability distribution: \begin{tabular}{c|ccccc} Payout (\$) & -6 & -4 & -2 & 0 & 2 \\ \hline Probability & 0.34 & 0.13 & 0.06 & 0.13 & 0.34 \end{tabular} Expected Value = $\square$ Round to the nearest hundredth.
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Solution

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Solution Steps

Step 1: Calculate the product of each payout and its corresponding probability.

We multiply each payout by its probability:

  • \(-6 * 0.34 = -2.04\)
  • \(-4 * 0.13 = -0.52\)
  • \(-2 * 0.06 = -0.12\)
  • \(0 * 0.13 = 0\)
  • \(2 * 0.34 = 0.68\)
Step 2: Sum the products calculated in Step 1.

Adding the products from Step 1: \(-2.04 + (-0.52) + (-0.12) + 0 + 0.68 = -2.04 - 0.52 - 0.12 + 0.68 = -2\)

Final Answer

The expected value of the winnings is \\(\boxed{-2.00}\\).

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