If we have a group of 5 men and 4 women and we select two at random, without replacement, then find the probability that one of each gender

Question

If we have a group of 5 men and 4 women and we select two at random, without replacement, then find the probability that one of each gender is selected

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Thanh Hà 5 months 2021-08-15T13:24:24+00:00 1 Answers 7 views 0

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    2021-08-15T13:26:14+00:00

    Answer:

    5/9

    Step-by-step explanation:

    If we have a group of 5 men and 4 women, the total number of people we have is 5+4 = 9 people

    Total outcome = 9people

    For us to select one of each gender without replacement and selecting two at random means we can select a male before a female or a female before a male.

    Let W =Women and M = Male

    The Probability of selecting two at random without repalcement is given as;

    = Pr(W)Pr(M) + Pr(M)Pr(W)

    = (4/9*5/8)+(5/9*4/8) (Note that the total number reduces by 1 during the second pick since we aren’t replacing the person we picked first)

    = 20/72 + 20/72

    = 40/72

    = 20/36

    = 5/9

    Hence the the probability that one of each gender is selected is 5/9

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