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March 25, 2017

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Claire takes a five-question true-false test. She hasn't studied, so she guesses at random. With her ESP she figures she has a 60% probability of getting any one answer wrong.

A. What is the probability of getting an answer wrong? (Do you think they want me to ignore the ESP nugget or take it into account?)
b. Let P(x) be the probability of getting exactly x of the five answers right. Calculate p(0) through P(5)
c. What is the probability of getting at least three answers right.

  • Math/Prob - ,

    We will have to assume the ESP estimation is correct.
    The resulting distribution is binomial, with 5 questions, and probability of success p=1-0.6=0.4, q=1-p=0.6 (failure).

    The probability of getting exactly n question correct (out of 5) is given by the binomial coefficient
    C(5,n)p^n q^(5-n)
    where C(5,n)=5!/(n!(5-n)!)
    Example:
    probability of getting 3 answers right
    =P(3) = [5!/(3!2!)]0.4^3 0.6^2
    =0.2304

    To calculate the probability of getting at least three correct would be:
    P(3)+P(4)+P(5)=0.317

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