Question

Ten percent of the engines manufactured on an assembly line are defective. If engines are randomly...

Ten percent of the engines manufactured on an assembly line are defective. If engines are randomly selected one at a time and tested. a) Find the probability that the third engine tested is the first non-defective engine. b) Find the probability that the 10th engine tested is the fourth non-defective engine. c) Find the probability that the third non-defective engine will be found on or before the sixth engine tested.

Homework Answers

Answer #1

a)

probability that the third engine tested is the first non-defective engine =P(first two are defective and third is first non-defective)=(0.1)2*0.9=0.009

b)

probability that the 10th engine tested is the fourth non-defective engine=P(3 non defective in first 9 and 4th non-defective engine on 10th)= =0.000055

c)

probability that the third non-defective engine will be found on or before the sixth engine tested

=1-P(till 6th engine at most 2 non-defective)

=1-(P(X=0)+P(X=1)+P(X=2))=1-()

=1-0.00127 =0.99873

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