According to a survey 60% of people have a dog. If 5 people are selected randomly, what is the probability that at least 2 of them have a do

Question

According to a survey 60% of people have a dog. If 5 people are selected randomly, what is the probability that at least 2 of them have a dog ? Round your answer to the nearest tenth of a percent .

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Liliana 3 hours 2021-09-15T00:18:40+00:00 1 Answer 0

Answers ( )

  1. Answer:

    Probability that at least 2 of them have a dog is 0.913.

    Step-by-step explanation:

    We are given that according to a survey 60% of people have a dog.

    Also, 5 people are selected randomly.

    The above situation can be represented through binomial distribution;

    P(X=r)=\binom{n}{r} \times p^{r}\times (1-p)^{n-r}; x = 0,1,2,3,.....

    where, n = number of trials (samples) taken = 5 people

                r = number of success

                p = probability of success which in our question is probability

                       that people have a dog, i.e; p = 60%

    Let X = Number of people who have a dog

    SO, X ~ Binom(n = 5, p = 0.60)

    Now, probability that at least 2 of them have a dog is given by = P(X \geq 2)

     P(X \geq 2) = 1 – P(X < 2)

                    = 1 – P(X = 0) – P(X = 1)

                    =  1-\binom{5}{0} \times 0.60^{0}\times (1-0.60)^{5-0}-\binom{5}{1} \times 0.60^{1}\times (1-0.60)^{5-1}        

                    =  1-(1 \times 1\times 0.40^{5})-(5\times 0.60^{1}\times 0.40^{4})

                    =  1 – 0.01024 – 0.0768

                    =  0.913

    Therefore, probability that at least 2 of them have a dog is 0.913.

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