Question

RicherNYou is a small automobile manufacturer specializes in custom-built automobiles. As a rule, the manufacturer buys the engines from Hoity-Toity Motors, where they are built to stringent specifications. A lot of 40 engines has just been received by the manufacturer, whose acceptance plan is to select eight engines at random and submit them to thorough testing. If none of the engines are found to have serious defects, RicherNYou will accept the lot; otherwise, the lot will be rejected. If the lot contains two engines with serious defects, what is the probability that the lot will be accepted under this acceptance plan?

Answer 1

Population:

   Defectives = 2

Non-defectives = 38

Total engines = 40

Sample:

   Defectives = 0

Non-defectives = 8

Total engines = 8

Number of ways of selecting 8 engines from 40 engines is given by:

Number of ways of selecting 8 non-defectives from 38 non-defectives is given by:

So,

the probability that the lot will be accepted under this acceptance plan = 48903492/76904685 = 0.6359

So,

Answer is:

0.6359