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

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;

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 2)

P(X 2) = 1 – P(X < 2)

= 1 – P(X = 0) – P(X = 1)

=

=

=  1 – 0.01024 – 0.0768

=  0.913

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