SOLUTION: In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacement. Suppose that six of the tanks contain material

Question 366805: In a chemical plant, 24 holding tanks are used for final product storage. Four tanks are selected at random and without replacement. Suppose that six of the tanks contain material in which the viscosity exceeds the customer requirements.
a) Define events
b) Write Givens
c) What is the probability that exactly one tank in the sample contains high viscosity material ?
d) What is the probability that at least one tank in the sample contains high viscosity material?
e) In addition to the six tanks with high viscosity levels, four different tanks contain material with high impurities. What is the probability that exactly one tank in the sample contains high viscosity material and exactly one tank in the sample contains material with high impurities?

Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
a & b)
6/24=.25 contain high visc. material.
18/24=.75 contain normal visc material.
Four tanks are selected at random and without replacement. Hypergeometric distribution since there is no replacement.
.
c)
(6C1 * 18C3)/24C4
=(6*816)/10626)
=.4608 the probability that exactly one tank in the sample contains high viscosity material .
.
d)
1-((6C0 * 18C4)/24C4)
=1-(3060/10626)
=1-.2880
=.7120 the probability that at least one tank in the sample contains high viscosity material.
.
e)
(4C1 * 6C1 * 14C2)/24C4
=(4*6*91)/10626
=.2055 the probability that exactly one tank in the sample contains high viscosity material and exactly one tank in the sample contains material with high impurities.
.
Ed

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