A (very bad) factory produces plastic bags such that 30% of the plastic bags produced are defective and 70% are good. A sample of 5 plastic

Question

A (very bad) factory produces plastic bags such that 30% of the plastic bags produced are defective and 70% are good. A sample of 5 plastic bags is selected at random. (a) What is the probability that all 5 bags selected are defective?

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Camila 2 hours 2021-09-13T02:41:35+00:00 1 Answer 0

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    2021-09-13T02:42:45+00:00

    Answer:

    0.24% probability that all 5 bags selected are defective

    Step-by-step explanation:

    For each bag, there are only two possible outcomes. Either they are defective, or they are not. The probability of a bag being defective is independent from other bags. 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.

    30% of the plastic bags produced are defective

    This means that p = 0.3

    A sample of 5 plastic bags is selected at random

    This means that n = 5

    What is the probability that all 5 bags selected are defective?

    This is P(X = 5). So

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

    P(X = 5) = C_{5,5}.(0.3)^{5}.(0.7)^{0} = 0.0024

    0.24% probability that all 5 bags selected are defective

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45:7+7-4:2-5:5*4+35:2 =? ( )