<PRE><B>Question 433452</B>
A company uses printer cartridges from three manufacturers. 
Manufacturers A, B, and C supply, respectively, 60%, 30%, and 10% of the company’s cartridges.
---------------------------------- 
1% of cartridges from A, 
2% from B, 
3% from C are defective. 
----------------------------------
P(d|A) = P(d and A)/P(A) = P(d and A)/0.6 = 0.01
----
P(d|B) = P(d and B)/P(B) = P(d and B)/0.3 = 0.02
----
P(d|C) = P(d and C)/P(C) = P(d and C)/0.1 = 0.03
----

If a cartridge is randomly chosen and found to be defective, what is the probability that it is from manufacturer C?
---
P(C|d) = P(C and d)/P(d)
---
= P(C and d)/[P(d and A)+P(d and B)+P(d and A)]
---
= [0.1*0.03)/[0.6*0.01+0.3*0.02+0.1*0.03]
---
= 0.003/0.015
----
= 0.2
================
Cheers,
Stan H.
---
</PRE>