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?
Answers
Given : A manufacturer supplies cheap motors in batches of size 25. tests at random a sample of 5 motors and accepts the lot if they are all good.
To find : Probability (a) he will accept a batch containing five defective motors? (b) he will reject (not accept) a lot containing only one defective motor?
Solution:
a) batch containing five defective motors
Total = 25
Defective = 5
non Defective = 20
5 pcs out of 25 can be selected in ²⁵C₅
Batch accepted if all non defective Selected
5 pcs out of 20 can be selected in ²⁰C₅
Probability = (²⁰C₅) / (²⁵C₅)
= 0.29
0.29 is the probability that he will accept a batch containing five defective motors
b) lot containing only one defective motor
Total = 25
Defective = 1
non Defective = 24
5 pcs out of 25 can be selected in ²⁵C₅
Batch rejected if one defective Selected and rest 4 Selected from non Defective
accepted if all 5 are selcted from 24 non defectives
4 pcs out of 24 can be selected in ²⁴C₄
Probability = (²⁴C₄) / (²⁵C₅) or 1 - (²⁴C₅) / (²⁵C₅) ( 1 - accepted )
= 0.2
0.2 is the probability he will reject (not accept) a lot containing only one defective motor
Learn more:
If the probability of selecting a defective bolt is 0.1, find (1) the mean ...
https://brainly.in/question/11773467
Find the probability that at least5 defective bolts will be foundin a ...
https://brainly.in/question/13165988
A box contains 100 bolts and 50 nuts. It is given that 40% bolts and ...
https://brainly.in/question/8398577