According to data from the American Medical Association, 10% of us are left handed. If three people are randomly selected, find the probabil

Question

According to data from the American Medical Association, 10% of us are left handed. If three people are randomly selected, find the probability that they are all left-handed. What probability distribution can we use to answer this question

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Hadley 4 weeks 2021-09-22T11:35:18+00:00 1 Answer 0

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    2021-09-22T11:36:55+00:00

    Answer:

    For each person, there are only two possible outcomes. Either they are left handed, or they are not. The probability of a person being left-handed is independent from other people. So we use the binomial probability distribution to solve this question.

    0.1% probability that they are all left-handed.

    Step-by-step explanation:

    For each person, there are only two possible outcomes. Either they are left handed, or they are not. The probability of a person being left-handed is independent from other people. So we use the binomial probability distribution to solve this question.

    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.

    10% of us are left handed.

    This means that p = 0.1

    If three people are randomly selected, find the probability that they are all left-handed.

    This is P(X = 3) when n = 3. So

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

    P(X = 3) = C_{3,3}.(0.1)^{3}.(0.9)^{0} = 0.001

    0.1% probability that they are all left-handed.

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