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6 April, 22:32

In a certain liberal arts college with about 10,000 students, 59% are males. If two students from this college are selected at random, what is the probability that they are of the same gender?

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  1. 6 April, 23:17
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    P (S) = 0.5162 or 51.62%

    the probability that they are of the same gender is 0.5162 or 51.62%

    Step-by-step explanation:

    The probability that the two selected students are of the same gender P (S) is;

    P (S) = Probability that they are both male P (M) + probability that they are both female P (F)

    P (S) = P (M) + P (F) ... 1

    Given;

    Proportion of male = 59% = 0.59

    Proportion of female = 1-0.59 = 0.41

    P (M) = 0.59*0.59 = 0.3481

    P (F) = 0.41 * 0.41 = 0.1681

    From equation 1;

    P (S) = 0.3481 + 0.1681

    P (S) = 0.5162 or 51.62%

    the probability that they are of the same gender is 0.5162 or 51.62%
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