Susan is taking Western Civilization this semester on a pass/fail basis. The department teaching the course has a history of passing 77% of the students in Western Civilization each term. Let represent the number of times a student takes Western Civilization until the first passing grade is received? (Assume the trials are independent.) a. Write out a formula for the probability distribution of the random variable.

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  1. P(n) = p(1-p)^(n-1), where p is the probability of success in each trial, and n is the number of trials.

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  2. Therefore, how to solve this problem is simple. If you have noticed, the question says, "Let represent the number of times a student takes Western Civilization until the first passing grade is received." The variable that is supposed to go in between the words 'Let' and 'represent' is n.

    The problem does not give us the value of n, so we will make one up for the sake of using the formula correctly.

    Assume, therefore, that n = 1, it takes the student only one try to pass Western Civilization.
    P is automatically assigned a value, which would be .77.

    So, using the formula, substituting the values becomes easy.

    P(1) = .77(1-.77)^(1-1)
    P(1) = .77 or 77%

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