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Answer: 0.299
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: $$P(X = x) = \binom{n}{x} p^x (1-p)^{n-x}$$ Calculating step by step: 1. Binomial coefficient: $$\binom{5}{2} = \frac{5!}{2!3!} = \frac{120}{2 \times 6} = \frac{120}{12} = 10$$ 2. $$p^x = 0.52^2 = 0.2704$$ 3. $$(1-p)^{n-x} = 0.48^3 = 0.110592$$ 4. Multiply: $$10 \times 0.2704 \times 0.110592 = 0.2990$$ Thus, the probability of selecting exactly two underpriced stocks during the week is 0.2990 or 29.90%.
Author: Nikitesh Somanthe
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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
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