Hello, Problem is 2-107: \"The probability that a lab specimen contains high lev

Question

Hello,
Problem is 2-107: "The probability that a lab specimen contains high levels ofcontamination is 0.10. Five samples are checked, and the samplesare independent."
b) What is the probability that exactly one contains highlevels of contamination?
In part (b) of this problem, the probability is multiplied by(5).
[(0.1)(0.9)(0.9)(0.9)(0.9)] * 5 = 0.33 to find the statisticalprobability that one contains a high level of contamination (with0.10 being the probability that one will contain a high level ofcontamination).
Why is this part multiplied by 5, butyet part A is not multiplied by 5?


Problem is 2-107: "The probability that a lab specimen contains high levels ofcontamination is 0.10. Five samples are checked, and the samplesare independent."
b) What is the probability that exactly one contains highlevels of contamination?
In part (b) of this problem, the probability is multiplied by(5).
[(0.1)(0.9)(0.9)(0.9)(0.9)] * 5 = 0.33 to find the statisticalprobability that one contains a high level of contamination (with0.10 being the probability that one will contain a high level ofcontamination).
Why is this part multiplied by 5, butyet part A is not multiplied by 5?

Explanation / Answer

p(contamination)=.1 In a sample of 5 the one contaminated specimem could be in thefirst, the second the third, the fourth or the fifthposition. Hence 5 positions. P(exactly one in findcontaminated)=5(.1)(.9)4 Another way of seeing this is that we have a binomialdistribution P(x=1)=C(5,1)(.1)1(.9)4=5(.1)(.9)4

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