Message posted by ALI HASSAN (via 203.135.54.28) on January 23, 2002 at 1:04 PM (ET)

SIR,

WILL YOU PLEASE SEND ME ANSWER OF THE FOLLOWING QUESTION.

Q. IN A FACTORY MACHINE A PRODUCES 60% OF THE OUTPUT AND MACHINE B PRODUCES 40%. ON THE AVERAGE 5 ITEMS IN 1000 PRODUCES BY A ARE DEFECTIVE AND 2 ITEMS IN 250 PRODUCED BY B ARE DEFECTIVE. AN ITEM DRAWN AT RANDOM FROM A DAY'S OUTPUT IS DEFECTIVE. WHAT IS THE PROBABILTY. THAT IT WAS PRODUCED BY A ? BY B ?

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re:
Message posted by Jack Tomsky (via 12.144.103.66) on January 24, 2002 at 2:02 PM (ET)

P(A|x) = Num/Den, where

Num = P(A)*P(x|A)
Den = P(A)*P(x|A) + P(B)*P(x|B)

P(A) = .6
P(B) = .4
P(x|A) = .005
P(x|B) = .008

Then P(B|x) = 1-P(A|x).