Respuesta :
Answer:
a) 0.6561
b) 0.2916
c) 0.3439
Step-by-step explanation:
We are given the following information:
Let us treat high level of contamination as our success.
p = P(High level of contamination) = P(success) = 0.10
n = 4
The, by binomial distribution:
[tex]P(X=x) = \binom{n}{x}.p^x.(1-p)^{n-x}\\\text{where x is the number of success}[/tex]
a) P(No high level of contamination)
We put x = 0, in the formula.
[tex]P(X=0) = \binom{4}{0}.(0.10)^0.(1-0.10)^{4} =0.6561[/tex]
Probability that no lab specimen contain high level of contamination is 0.6561
b) P(Exactly one high level of contamination)
We put x = 1, in the formula.
[tex]P(X=1) = \binom{4}{1}.(0.10)^1.(1-0.10)^{3} =0.2916[/tex]
Probability that no lab specimen contain high level of contamination is 0.6561
c) P(At least one contains high level of contamination)
[tex]p(x \geq 1) = 1 - p( x = 0) = 1 - 0.6561 = 0.3439[/tex]
Probability that at least 1 lab specimen contain high level of contamination is 0.3439
