Financial Risk Manager Part 1

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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?

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TTanishq

0.395

0.208

0.327

0.299

Explanation:

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:

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.

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