Question
If a machine is correctly set up, it produces 90% acceptable items. If it is incorrectly set up, it produces only 40% acceptable items. Past experience shows that 80% of the set ups are correctly done. If after a certain set up, the machine produces 2 acceptable items, find the probability that the machine is correctly setup.
Solution
Let A be the event that the machine produces 2 acceptable items.
Again, let B1 represent the event of correct setup and B2 represent the event of incorrect setup.
Now, 
