To calculate the expected value of Rachel's winnings from the card game, we need to identify the probabilities and the corresponding winnings for each card.
Assuming Rachel randomly selects one of three cards (A, B, or C), each card has an equal probability of being selected. This means:
- Probability of selecting Card A = \( \frac{1}{3} \)
- Probability of selecting Card B = \( \frac{1}{3} \)
- Probability of selecting Card C = \( \frac{1}{3} \)
Now let's assign the winnings for each card as follows:
- Winnings from Card A = $10
- Winnings from Card B = $15
- Winnings from Card C = $50
Now we can calculate the expected value (EV) using the formula:
\[ \text{EV} = (P(A) \times W(A)) + (P(B) \times W(B)) + (P(C) \times W(C)) \]
Substituting in the probabilities and winnings:
\[ \text{EV} = \left(\frac{1}{3} \times 10\right) + \left(\frac{1}{3} \times 15\right) + \left(\frac{1}{3} \times 50\right) \]
Calculating each term:
\[ \text{EV} = \frac{10}{3} + \frac{15}{3} + \frac{50}{3} = \frac{10 + 15 + 50}{3} = \frac{75}{3} = 25 \]
Thus, the expected value of Rachel's winnings is $25.
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