5.27.2005

Q&A: What's the probability that the student passes the interview test?

There are 5 multiple choice questions on an interview test, each having 4 answers. Each question is worth 5 points and only one answers per question is correct. To pass the test one needs at least 20 points. Suppose the student guesses the answer to each question, and his or her guesses from question to question are independent.

A: This is similar to the coin flipping problem (i.e what is the probability of obtaining exactly 4 heads if a fair coin is flipped 5 times) except in this case the probably is not 1/2.

  • to get at least 20 points, one must get at least 4 questions right. so we are interested in P(X>=4)
    • The random variable X is binomial with n = 5 and p = 0.25 (4 choices)
  • P(X>=4) = P(4) + P(5) = 0.0155.
    • P(4) = C(4, 5) * p^4 * (1-p)^(5-4) = {5!/[(5 - 4)! x 4!]} * 0.25^4 * (1-0.25)^(5-4) = 0.0146. Or with Excel,
      • P(4) = ( fact(5)/(fact(5-4)*fact(4)) ) * 0.25^4 * (1-0.25)^(5-4)
      • P(4) = BINOMDIST(4,5,0.25,FALSE)
    • P(5) = BINOMDIST(5,5,0.25,FALSE) = 0.0009

Bonus Points

  • For a binomial random variable, the probability, p, of success must be constant for all trials, and the trials are independent.

Category: C++ Quant > Quantitative Analysis > Probability

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