Q29 of 29 Page 1

The members of a consulting firm rent cars from three rental agencies: 50% from agency X, 30% from agency Y and 20% from agency Z. From past experience it is known that 9% of the cars from agency X need a service and tuning before renting, 12% of the cars from agency Y need a service and tuning before renting, and 10% of the cars from agency Z need a service and tuning before renting. If the rental car delivered to the firm needs service and tuning, find the probability that agency Z is not to be blamed.

Let A be the event that car delivered to firm needs service and tuning.


Also, let E1, E2 and E3 be the events of car being rented from agencies X, Y and Z respectively.


Probability of car being rented from x=



Probability of car being rented from y=



Probability of car being rented from z=



Also,





We know from Bayes’ theorem,







We know that P(a’) = 1 – P(a), so,




Hence,


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