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14 October, 16:14

The United States, 44% of the population has type A blood. Consider taking a sample of size 4. Let Y denote the number of persons in the sample with type A blood. Find pr[Y = 0}. pr{ Y=1}. Pr{Y = 2}.

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  1. 14 October, 18:05
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    pr{Y=0} = 9,8%

    pr{Y=1} = 30.9%

    pr{Y=2} = 36%

    Step-by-step explanation:

    The probability of each person in the sample having type A blood in independent from each other. So, the first person will have a 44% chance of having type A blood, and so will the second, the third and the fourth.

    So, the first question.

    a) pr{Y = 0}

    The probability of each of the four people having non-type A blood is 56%.

    So, pr{Y=0} = 0.56*0.56*0.56*0.56 = 0.098 = 9,8%.

    b) pr{Y=1}

    All of the following order of samples satisfy the condition

    A - NA - NA - NA

    NA - A - NA - NA

    NA - NA - A - NA

    NA - NA - NA - A

    Since the probabilties are independent, each order has the following probability P.

    P = 0.44 * (0.56) ^{3} = 0.0773

    Since there are four possible orders, pr{Y=1} = 4*P = 0.309 = 30.9%

    c) pr{Y=2}

    All of the following order of samples satisfy the condition:

    A - A - NA - NA

    A - NA - A - NA

    A - NA - NA - A

    NA - A - A - NA

    NA - A - NA - A

    NA - NA - A - A

    Each order has the following probability P.

    P = (0.44) ² * (0.56) ² = 0.06

    Since there are six possible orders, pr{Y = 2} = 6*P = 0.36 = 36%
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