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)![]() ![]() You can put this solution on YOUR website! 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? \n" ); document.write( " \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 \n" ); document.write( " \n" ); document.write( " |