SOLUTION: Suppose that a certain college class contains 65 students. Of these, 37 are juniors, 38 are history majors, and 5 are neither. A student is selected at random from the class. (a)

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Question 1174934: Suppose that a certain college class contains 65 students. Of these, 37 are juniors, 38 are history majors, and 5 are neither. A student is selected at random from the class. (a) What is the probability that the student is both a junior and a history major? (b) Given that the student selected is a junior, what is the probability that he is also a history major?
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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(a) From one side,  P(or) = 1 - 5%2F65 = 60%2F65.


    From the other side,


        P(or) = P(junior) + P(history) - P(both),

    or

       60%2F65 = 37%2F65 + 38%2F65 - P(both).


    THEREFORE,

       P(both) = 37%2F65+%2B+38%2F65+-+60%2F65 = 15%2F65 = 3%2F13.    ANSWER



(b)   P(junior|history) = P%28both%29%2FP%28history%29 = %28%283%2F13%29%29%2F%28%2838%2F65%29%29 = %28%2815%2F65%29%29%2F%28%2838%2F65%29%29 = 15%2F38.    ANSWER

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