Question

8 of the 40 newly built cars are selected at random to be checked for steering defects. Suppose 10 of the cars have such defects. What is the probability that all 8 of the selected cars have steering defect?

Answer 1

Since you are sampling without replacement and the sample size is large with respect to the population `(8/40=20%)`, use the following "counting" method ...

Explanation:

Number of ways to select 8 of the 10 defects :

`=(10!)/(8!xx2!)=45` ways

In general , number of ways to select 8 from a population of 40:

`=(40!)/(8!xx32!)=76,904,685` ways

Finally, calculate your probability ...

`P("all 8 have defects")=45/(76,904,685)~~0.000000585`

hope that helped