SOLUTION: 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 Compa
Algebra.Com
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
RELATED QUESTIONS
In a recent production of automobiles, 10% are found to have a minor engine defect. A... (answered by 296714)
The members of a consulting firm rent cars from 3 rental companies: 60 percent from... (answered by jorel1380)
A women's clothing store owner buys from three companies: A, B and C. The most recent... (answered by stanbon)
A manufacture of air-conditioning units purchases 70% of its thermostats from company A,... (answered by ikleyn)
A company owns a fleet of trucks and cars. The ratio of trucks to cars is 1:3 and there... (answered by solver91311)
A credit card company decides to study the frequency with which its cardholders charge... (answered by stanbon)
A truck can be rented from Company A for $110 a day plus $0.60 per mile. Company B... (answered by stanbon)
A truck can be rented from Company A for $130 a day plus $0.60 per mile. Company B... (answered by richwmiller)
A truck can be rented from Company A for $70 a day plus $0.60 per mile.... (answered by jorel1380)