Problem 93E

Refer to Exercise 3.92. What is the probability that the third non-defective engine will be found

a on the fifth trial?

b on or before the fifth trial?

Reference

Ten percent of the engines manufactured on an assembly line are defective. If engines are randomly selected one at a time and tested, what is the probability that the first non-defective engine will be found on the second trial?

Solution

Step 1 of 2

a) We have to find the probability of finding 3rd non-defective engine in the fifth trial

Given that 10% of the engines are defective

And 90% of the engines are non defectives

Then p=0.9

And q=1-0.9

=0.1

The pmf of negative binomial distribution for n trials, given k success is

Here n=5

k=3

=(0.729)(0.01)

=0.04374

Hence the probability of finding 3rd non-defective engine in the fifth trial is 0.04374