Question 1088324: A rental company purchases cars from two dealerships. 75% of the vehicles are purchased from Company A and 25% from Company B. During the first year, 16% of the vehicles from Company A require major repairs. 20% from Company B require major repairs. If a car is chosen at random, what is the probability that it will require major repairs in the first year?
Answer by mathmate(429)   (Show Source):
You can put this solution on YOUR website! Question:
A rental company purchases cars from two dealerships. 75% of the vehicles are purchased from Company A and 25% from Company B. During the first year, 16% of the vehicles from Company A require major repairs. 20% from Company B require major repairs. If a car is chosen at random, what is the probability that it will require major repairs in the first year?
Solution:
The two companies are complementary in the sale of vehicles.
Let
R=event that the vehicle requires repairs.
Assuming random choice of vehicles among the two dealerships, then the probability of repairs can be estimated by the law of total probability:
P(R)=∑piP(i)
where
P(i) is the probability of choosing dealership i
pi is the probability of vehicles from dealership i requiring repairs.
Here
P(A)=0.75, pA=0.16
P(B)=0.25, pB=0.20
so
P(R)=0.75*0.16+0.25*0.20=0.12+0.05=0.17
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