SOLUTION: Research has shown that, for a certain company, 7% of plant A products are defective, 92% of plant B products are non-defective, 10% of plant C products are defective, and 95% of p

Algebra ->  Probability-and-statistics -> SOLUTION: Research has shown that, for a certain company, 7% of plant A products are defective, 92% of plant B products are non-defective, 10% of plant C products are defective, and 95% of p      Log On


   

Question 1047566: Research has shown that, for a certain company, 7% of plant A products are defective, 92% of plant B products are non-defective, 10% of plant C products are defective, and 95% of plant D products are non-defective. Of all the products manufactured by this company, 15% come from plant A, 25% from plant B, and 48% from plant C. An inspector has just randomly selected one product from the warehouse of this company.
(a) What is the probability that it is defective? [10]
(b) If it is defective, what is the probability that it came from plant B? [5]
(c) If it is non-defective, what is the probability that it came from plant D? [10]
Found 2 solutions by Boreal, ewatrrr:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Make the total 1000
========defective==========non-defective======total
A-----------10.5===============139.5==========150
B========20================230===========250
C========48================432 ==========480
D=========6================114===========120
Total======84.5==============915.5=========1000
Probability it is defective is 8.45%, total defective over total
If defective, probability it came from B is 20/84.5 or 23.7%
If non-defective, probability it came from D is 114/915.5=12.5%

Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!


Hi  

Perhaps this table will help:

#	 p	n*p	

0.15	0.07	0.0105	A

0.25	0.08	0.02	B

0.48	0.10	0.048	C

0.02	0.05	0.001	D

		0.0795	SUM