document.write( "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? \n" ); document.write( "
Algebra.Com's Answer #702925 by mathmate(429)\"\" \"About 
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Question:
\n" ); document.write( "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?
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\n" ); document.write( "Solution:
\n" ); document.write( "The two companies are complementary in the sale of vehicles.
\n" ); document.write( "Let
\n" ); document.write( "R=event that the vehicle requires repairs.
\n" ); document.write( "Assuming random choice of vehicles among the two dealerships, then the probability of repairs can be estimated by the law of total probability:
\n" ); document.write( "P(R)=∑piP(i)
\n" ); document.write( "where
\n" ); document.write( "P(i) is the probability of choosing dealership i
\n" ); document.write( "pi is the probability of vehicles from dealership i requiring repairs.
\n" ); document.write( "Here
\n" ); document.write( "P(A)=0.75, pA=0.16
\n" ); document.write( "P(B)=0.25, pB=0.20
\n" ); document.write( "so
\n" ); document.write( "P(R)=0.75*0.16+0.25*0.20=0.12+0.05=0.17
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