Q. 305.0( 3 Votes )

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 setups are correctly done. If after a certain set up, the machine produces 2 acceptable items, find the probability that the machine is correctly set up.

Answer :

Let us assume U1, U2 and A be the events as follows:


U1 = Machine is correctly set up


U2 = Machine is incorrectly set up


A = produce two acceptable items


From the problem




P(A|U1) = P(producing 2 acceptable items if machine is correctly set up)




P(A|U2) = P(producing 2 acceptable items if machine is not correctly set up)




Now we find


P(U1|A) = P(Machine is correctly set up for producing 2 acceptable items)


Using Baye’s theorem:







The required probability is .


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