Question
A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?
Solution
Let E1, E2, E3, E be the events
E1 : ‘Item is produced by operator A’,
E2 : ‘Item is produced by operator B’,
E3 : ‘Item is produced by operator C’,
E : ‘Item chosen is found defective’
Required probability = 
(By Baye's Theorem)
