Question

The probability that a lab specimen contains high levels of contamination is 0.12. A group of 4 independent samples are checked. Round your answers to four decimal places (e.g. 98.7654). (a) What is the probability that none contain high levels of contamination

Answer 1

0.5996 is the probability that none contain high levels of contamination.

Explanation:

We are given the following information:

We treat lab specimen containing high levels of contamination as a success.

P( lab specimen containing high levels of contamination) = 0.12

Then the number of lab specimens 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 = 4

We have to find the probability that none of the lab specimen consist of high level of contamination.

We have to evaluate:

`P(x = 0)\\= \binom{4}{0}(0.12)^0(1-0.12)^((4-0))\\= 0.5996`

0.5996 is the probability that none contain high levels of contamination.