Q. 485.0( 1 Vote )

An item is manufa

Answer :

Let events E1, E2, E3 be the following:

E1: event that item is manufactured by machine A


E2: event that item is manufactured by machine B


E3: event that item is manufactured by machine C


Clearly, E1, E2 and E3 are mutually exclusive and exhaustive events and hence, they represent a partition of sample space.


Given that:


Items manufactured on machine A = 50%


Items manufactured on machine B = 30%


Items manufactured on machine C = 20%


So,



Now, Let E be the event that ‘an item is defective’.


P(E|E1) is the probability of the item drawn is defective given that it is manufactured on machine A = 2%


P(E|E2) is the probability of the item drawn is defective given that it is manufactured on machine B = 2%


P(E|E3) is the probability of the item drawn is defective given that it is manufactured on machine C = 3%


So,


Now, we have to find the probability that the item which is picked


up is defective, it was manufactured on machine A


We use Bayes’ theorem to find the probability of occurrence of an event A when event B has already occurred.



P(E1|E) is the probability that the item is drawn is defective and it was manufactured on machine A








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