Question

The probability that a lab specimen contains high levels of contamination is 0.10. A group of 3 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? (a) .729

Answer 1

(a) 0.7290 or 72.90%

(b) 0.2430 or 24.30%

(c) 0.2710 or 27.10%

Explanation:

Probability of contamination = 0.10

Sample size = 3

(a) The probability that none of the three contain high levels of contamination is:

`P(X=0) = (1-0.10)^3\\P(X=0)=0.7290 = 72.90\%`

The probability is 0.7290 or 72.90%.

(b) The probability that exactly one of the three contains high levels of contamination is:

`P(X=1) = 3*(1-0.10)^2*0.10\\P(X=1) = 0.2430=24.30\%`

The probability is 0.2430 or 24.30%.

(c) The probability that at least one contains high levels of contamination is:

`P(X\geq1) = 1-P(X=0) = 1-0.7290\\P(X\geq1) =0.2710 = 27.10\%`

The probability is 0.2710 or 27.10%.