Question

According to a survey, 29% of people carry at least 1 reusable water bottle. If 5 people are selected randomly, what is the probability that at least 2 of them will be carrying a reusable water bottle? Round your answer to the nearest tenth of a percent.

Answer 1

Answer:

0.4 is the probability that at least 2 out of 5 will be carrying a reusable water bottle

Step-by-step explanation:

We are given the following information:

We treat people carrying at least 1 reusable water bottle as a success.

P(people carry at least 1 reusable water bottle) = 29% = 0.29

Then the number of people follows a binomial distribution, where

$P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}$

where n is the total number of observations, x is the number of success, p is the probability of success.

Now, we are given n = 5

We have to evaluate:

$P(x \geq 2) =1- P(x < 2) \\=1 - \binom{5}{0}(0.29)^0(1-0.29)^5 + \binom{5}{1}(0.29)^1(1-0.29)^4\\=1- 0.1804 - 0.3684\\= 0.4512\\\approc 0.4$

0.4 is the probability that at least 2 out of 5 will be carrying a reusable water bottle