Answer:
(a) 0.7290 or 72.90%
(b) 0.2430 or 24.30%
(c) 0.2710 or 27.10%
Step-by-step explanation:
Probability of contamination = 0.10
Sample size = 3
(a) The probability that none of the three contain high levels of contamination is:
[tex]P(X=0) = (1-0.10)^3\\P(X=0)=0.7290 = 72.90\%[/tex]
The probability is 0.7290 or 72.90%.
(b) The probability that exactly one of the three contains high levels of contamination is:
[tex]P(X=1) = 3*(1-0.10)^2*0.10\\P(X=1) = 0.2430=24.30\%[/tex]
The probability is 0.2430 or 24.30%.
(c) The probability that at least one contains high levels of contamination is:
[tex]P(X\geq1) = 1-P(X=0) = 1-0.7290\\P(X\geq1) =0.2710 = 27.10\%[/tex]
The probability is 0.2710 or 27.10%.
