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6 August, 04:43

Suppose that A and B each randomly, and independently, choose 3 of 10 objects. Find the expected number of objects (a) chosen by both A and B; (b) not chosen by either A or B; (c) chosen by exactly one of A and B.

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  1. 6 August, 07:47
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    a) N (A∩B) = 0.9

    b) N (A∩B) = 4.9

    c) N (A or B) = 4.2

    Step-by-step explanation:

    Given that A and B each randomly, and independently, choose 3 of 10 objects;

    P (A) = P (B) = 3/10 = 0.3

    P (A') = P (B') = 1 - 0.3 = 0.7

    a) chosen by both;

    Probability of being chosen by both;

    P (A∩B) = 0.3 * 0.3 = 0.09

    Expected Number of objects being chosen by both;

    N (A∩B) = P (A∩B) * N (total) = 0.09*10

    N (A∩B) = 0.9

    b) not chosen by either A or B;

    Probability of not being chosen by either A or B;

    P (A'∩B') = 0.7 * 0.7 = 0.49

    Expected Number of objects being chosen by both;

    N (A'∩B') = P (A'∩B') * N (total) = 0.49*10

    N (A∩B) = 4.9

    c) chosen by exactly one of A and B.

    Probability of being chosen by exactly one of A and B

    P (A∩B') + P (A'∩B) = 0.3*0.7 + 0.7 * 0.3 = 0.42

    Expected Number of objects being chosen by both;

    N (A or B) = 0.42 * 10

    N (A or B) = 4.2
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