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CFA Level 1 Question of the Week - Quantitative Methods

Matt_AnalystPrepMatt_AnalystPrep MontrealPosts: 141 Associate
edited April 2017 in Level 1 Questions
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:

CFA Level 1 Question of the Week - Quantitative Methods 6 votes

A. 39.5%
0% 0 votes
B. 20.8%
16% 1 vote
C. 29.9%
83% 5 votes

Comments

  • Who can explain this? Plz tell me
  • 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)
    = 0.2990

    where
    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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