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

The memers of a consulting firm rent cars from three rental agencies:

1.	The memers of a consulting firm rent cars from three rental agencies: 50% from agency X, 20% from agency Y and 20% from agency Z. Form past experience, it is known that 9% of the cars from agency X need a service and tuning before renting, 12% of 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 need service and tuning, find the probability that agency Z is not to be blamed.
Answer» The memers of a consulting firm rent cars from three rental agencies: 50% from agency X, 20% from agency Y and 20% from agency Z. Form past experience, it is known that 9% of the cars from agency X need a service and tuning before renting, 12% of 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 need service and tuning, find the probability that agency Z is not to be blamed.