Questions: Find the expected value of the winnings from a game that has the following payout probability distribution:
Payout () 0 2 5 10 25
Probability 0.61 0.24 0.10 0.04 0.01
Expected Value =
Transcript text: Find the expected value of the winnings from a game that has the following payout probability distribution:
\begin{tabular}{c|ccccc}
Payout (\$) & 0 & 2 & 5 & 10 & 25 \\
\hline Probability & 0.61 & 0.24 & 0.10 & 0.04 & 0.01
\end{tabular}
Expected Value $=$ $\square$
Solution
Solution Steps
To find the expected value of the winnings from the game, we need to multiply each payout by its corresponding probability and then sum these products.
Step 1: Define the Payouts and Probabilities
We are given the payouts and their corresponding probabilities:
Payout ($)Probability00.6120.2450.10100.04250.01
Step 2: Calculate the Expected Value
The expected value E of the winnings is calculated using the formula:
E=i=1∑n(xi⋅pi)
where xi are the payouts and pi are the corresponding probabilities.
Substituting the given values:
E=(0⋅0.61)+(2⋅0.24)+(5⋅0.10)+(10⋅0.04)+(25⋅0.01)