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Answer: 0.299
## Explanation This is a binomial probability problem where: - **n = 5** (number of trials/days) - **x = 2** (number of successes/underpriced stocks) - **p = 0.52** (probability of success) - **q = 1 - p = 0.48** (probability of failure) The binomial probability formula is: $$P(X = x) = \binom{n}{x} p^x (1-p)^{n-x}$$ Substituting the values: $$P(X = 2) = \binom{5}{2} \cdot 0.52^2 \cdot 0.48^3$$ **Step-by-step calculation:** 1. **Combination term:** $$\binom{5}{2} = \frac{5!}{2! \cdot 3!} = \frac{120}{12} = 10$$ 2. **Probability terms:** $$0.52^2 = 0.2704$$ $$0.48^3 = 0.110592$$ 3. **Final calculation:** $$P(X = 2) = 10 \times 0.2704 \times 0.110592 = 0.2990$$ Therefore, the probability of selecting exactly two underpriced stocks during the week is **0.299**, which corresponds to option D.
Author: Tanishq Prabhu
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A trader purchases one single stock every day during five working days. His risk manager believes that the probability of selecting an underpriced stock at any given time is 52%. Assuming a binomial distribution, what is the probability of selecting exactly two underpriced stocks during the week out of the universe of underpriced and overpriced stocks?
A
0.395
B
0.208
C
0.327
D
0.299