Based on a​ poll, among adults who regret getting​ tattoos, 25​% say that they were too young when they got their tattoos. Assume that four

Question

Based on a​ poll, among adults who regret getting​ tattoos, 25​% say that they were too young when they got their tattoos. Assume that four adults who regret getting tattoos are randomly​ selected, and find the indicated probability. Complete parts​ (a) through​ (d) below.
a. Find the probability that none of the selected adults say that they were too young to get tattoos.

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Kiệt Gia 3 years 2021-08-21T20:32:39+00:00 1 Answers 5 views 0

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  1. quangkhai
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    2021-08-21T20:33:52+00:00
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    Answer:

    0.3164 = 31.64% probability that none of the selected adults say that they were too young to get tattoos.

    Step-by-step explanation:

    For each adult, there are only two possible outcomes. Either the say their were too young to get tattoos, or they do not say it. The answers for each adult is independent, which means that the binomial probability distribution is used 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.

    25​% say that they were too young when they got their tattoos.

    This means that p = 0.25

    Four adults who regret getting tattoos are randomly​ selected

    This means that n = 4

    a. Find the probability that none of the selected adults say that they were too young to get tattoos.

    This is P(X = 0). So

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

    P(X = 0) = C_{4,0}.(0.25)^{0}.(0.75)^{4} = 0.3164

    0.3164 = 31.64% probability that none of the selected adults say that they were too young to get tattoos.

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