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11 February, 23:29

63 % of men consider themselves professional baseball fans. You randomly select 10 men and ask each if he considers himself a professional baseball fan. Find the probability that the number who consider themselves baseball fans is (a) exactly five, (b) at least six, and (c) less than four.

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  1. 12 February, 03:22
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    a. 0.00069

    b. 0.063

    c. 0.00095

    Step-by-step explanation:

    a. Probability that exactly 5 men consider themselves professional baseball fans:-

    Here, there's a 63/100 or 63% possiblity that five (5) men consider themselves fans and of course, a 37/100 possibility that the other 5 men consider themselves non fans. Each of these must be multiplied and then the result will be the probability that exactly five men consider themselves baseball fans:-

    (63/100) ^5 * (37/100) ^5

    = 0.09924 * 0.006934

    = 0.000688

    Therefore the probability that 5 consider themselves baseball fans is 0.00069

    b. The probability that at least 6 are fans:-

    In this case, each of the 6 men have some 63/100 or 63% possibility of being a fan.

    We therefore multiply 63/100 by itself up to six times

    i. e 63/100 * 63/100 * 63/100 * 63/100 * 63/100 * 63/100

    or (63/100) ^6

    = 0.06252

    The probability that at least 6 men consider themselves professional baseball fans is 0.063

    c. Probability that less than four consider themselves baseball fans:-

    In this scenario, it means that at least 7 men out of the ten do not consider themselves professional baseball fans. We then simply multiply 37/100 by itself up to seven times. It isn't too necessary what the remaining three are.

    = (37/100) ^7

    = 0.0009493

    Therefore the possibility that less than four men do not consider themselves baseball fans is 0.00095
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