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6 August, 05:49

g A trial jury of 6 people is selected from 20 people: 8 women and 12 men. What is the probability that the jury will have an odd number of women

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  1. 6 August, 06:06
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    Answer: P (odd) = 0.499

    Step-by-step explanation:

    Given:

    Total number of people = 20

    Number of men = 12

    Number of women = 8

    Number of jury to be selected = 6

    For the jury to have an odd number of women. it must have either of the three.

    1. 1 woman, 5 men

    2. 3 women, 3 men

    3. 5 women, 1 man

    The total possible ways of selecting the 6 people jury is;

    N = 20C6 = 20!/6! (20-6) !

    N = 38760

    The possible ways of selecting;

    Case 1 : 1 woman, 5 men

    N1 = 8C1 * 12C5

    N1 = 8 * 792 = 6336

    Case 2 : 3 women, 3 men

    N2 = 8C3 * 12C3

    N2 = 12320

    Case 3 : 5 women, 1 man

    N3 = 8C5 * 12C1

    N3 = 672

    P (Odd) = (N1+N2+N3) / N

    P (odd) = (6336+12320+672) / 38760

    P (odd) = 19328/38760

    P (odd) = 0.499
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