In New York City, 45% of all blood donors have type O blood. (Based on data from the Greater New York Blood Program). Find the probability t

Question

In New York City, 45% of all blood donors have type O blood. (Based on data from the Greater New York Blood Program). Find the probability that 5 randomly selected blood donors in NYC all have Group O blood.

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Faith 1 week 2021-11-24T03:26:26+00:00 1 Answer 0 views 0

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    2021-11-24T03:27:41+00:00

    Answer:

    0.0185 = 1.85% probability that 5 randomly selected blood donors in NYC all have Group O blood.

    Step-by-step explanation:

    For each donor, there are only two possible outcomes. Either they have type O blood, or they do not. The donors are selected randomly, which means that the probability of a donor having type A blood is independent from other donors. So we use the binomial probability distribution to solve this problem.

    Binomial probability distribution

    The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

    C_{n,x} = \frac{n!}{x!(n-x)!}

    And p is the probability of X happening.

    In New York City, 45% of all blood donors have type O blood.

    This means that p = 0.45.

    Find the probability that 5 randomly selected blood donors in NYC all have Group O blood.

    This is P(X = 5) when n = 5. So

    P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

    P(X = 5) = C_{5,5}.(0.45)^{5}.(0.55)^{0} = 0.0185

    0.0185 = 1.85% probability that 5 randomly selected blood donors in NYC all have Group O blood.

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