Question

A manufacturer supplies cheap motors in batches of size 25. A buyer, before taking a batch, tests at random a sample of 5 motors and accepts the lot if they are all good. What is the probability that :
(a) he will accept a batch containing five defective motors?
(b) he will reject (not accept) a lot containing only one defective motor?

Answer 1

Answer:

Step-by-step explanation:

(a)Here we in the first scenario in he must pick 5 good motors out of the good motors entirely so that the batch gets selected.

So the number of good motors = 20

Total number of motors = 25

So the number of ways to pick out of the 5 good motors is the (20/25)* (19/24)*(18/23)*(17/22)*(16/21)*(15/25).

So here we can take 20 good items out of 25 and then 19 good items out of 24 and so on.

(b)If it contains one random defective motor then he must select it.

So here he will select one defective motor so it will be (1/25)*(24/24)*(23/23)*(22/22)*(21/21)

He would have to pick four good motors so that's why he can pick 24 good motors out 24 remaining.