Question

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.

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