Question

The probability that a lab specimen contains high levels of contamination is 0.10. A group of 5 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?
(b) What is the probability that exactly one contains high levels of contamination?
(c) What is the probability that at least one contains high levels of contamination?

Answer 1

Answer with Step-by-step explanation:

In case of Bernoulli trails

The probability that a random variable occurs 'r' times in 'n' trails is given by

`P(E)=\binom{n}{r}p^r(1-p)^(n-r)`

where

'p' is the probability of success of the event

Part a)

probability that no contamination occurs can be found by putting r = 0

Thus we get

`P(E_1)=\binom{5}{0}0.1^0(1-0.1)^(5)=0.5905`

part b)

The probability that at least 1 contamination occurs is given by

`P(E)=1-(1-p)^(n)`

Applying values we get

`P(E_2)=1-(1-0.1)^(5)=0.4096`