30. You want to simulate an experiment to draw cards out of a deck. You
plan to draw 35 cards (with replacement), and list which card you drew. How
many times would you expect to draw a face card?


  1. Using the binomial distribution, we have that you would expected to draw a face card 8 times.

    What is the binomial probability distribution?

    It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.
    The expected value of the binomial distribution is:
    E(X) = np
    For this problem, the parameters are given as follows:
    • n = 35, as the experiment will be repeated 35 times.
    • p = 0.2308, as of the 52 cards, there are 12 faces, hence 12/52 = 0.2308.
    Then the expected value is found as follows:
    E(X) = np = 35 x 0.2308 = 8
    You would expected to draw a face card 8 times.
    More can be learned about the binomial distribution at


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