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, the probability of selecting exactly two underpriced stocks during the week out of the universe of underpriced and overpriced stocks is closest to:
- A. 39.5%
- B. 20.8%
- C. 29.9%
The correct answer is C.
Since it’s a binomial distribution, we will solve the question with the help of the Bernoulli trial method.
The probability of having exactly 2 underpriced stocks in 5 trials (5 days), given that the probability of selecting an underpriced stock at any time is 52%, can be expressed as:
(n!/x!*(n-x)!) * p^x * (1 – p)^(n-x)
= 5!/(2!*3!) * 0.52^2 * (1 – 0.52)^3
= (120/12) * 0.2704 * (0.110592)
n is the number of trials;
x is the number of days having purchased an underpriced stock; and
p is the probability of selecting an underpriced stock.
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