Respuesta :
Answer:
a) There is a 61,41% of none of the samples containing high levels of contamination.
b)There is a 32.52% probability that exactly one sample contains high levels of contamination.
c) There is a 38.59% probability that at least one contains high levels of contamination
Step-by-step explanation:
The probabilities are independent from each other. It means that the probability of selecting a lab specimen being contaminated is always 15%, no matter how many contaminated lab specimen have been chosen.
a) There are 3 independent samples. For each sample, the probability of it not being contaminated is 85%. So, the probability that none of the sample are contaminated is
[tex]P = (0.85)^3 = 0.6141 = 61,41%[/tex]
There is a 61,41% of none of the samples containing high levels of contamination.
b) There are 3 independent samples. For each sample, the probability of it being contaminated is 15% and not contaminated 85%.
So the probability the exactly one sample contains high levels of contamination is:
[tex]P = (0.85)^2(0.15) = 0.1084 = 10,84%[/tex]
There can be 3 orderings of the sample in these conditions.(C-NC-NC, NC-C-NC, NC-NC,C), so the probability that exactly one contains high levels of contamination is
P = 3*0.1084 = 0.3252 = 32.52%.
There is a 32.52% probability that exactly one sample contains high levels of contamination.
c) The sum of the probabilities is always 100%.
In relation to the existence of a contaminated sample, either:
-None of the samples are contaminated.
-At least one of the samples are contaminated.
So, the probability of at least one of the samples being contaminated is 100% - the probability that none of the samples are contaminated, that we have already found in a).
So, it is
100% - 61.41% = 38.59%
There is a 38.59% probability that at least one contains high levels of contamination
