Suppose WMU has a fleet of vehicles The cars are 40 Fords 40

Suppose WMU has a fleet of vehicles. The cars are 40% Fords, 40% Chevys, and 20% Toyotas. After checking maintenance logs, it was found that 5% of the Fords, 3% of the Chevys and 8% of the Toyotas were \"lemons\" - they did work properly when they were new. Find the probability that any car chosen is a lemon. If a car chosen at random is a lemon, what is the probability that it is a Ford? If a car chosen at random is American, what is the probability that it is a lemon?

Solution

P(F) = 0.40
P(C) = 0.40
P(T) = 0.20
P(F n L) = 5% of 40 = 5*40/100 = 2
P(C n L) = 3% of Chev = 3*40/100 = 3*20/50 = 1.2
P(T n L) = 8% of Toyota = 8*20/100 = 1.6
P(L) = 2 + 1.2 + 1.6 = 4.8

a)
P( Car chosen is a Lemon) = 4.8/100 = 0.048
b)
P( Car is a lemon given that it is Ford) = P( L n F)/P(F) = 2/40 = 1/20 = 0.05

c)
not possible to calculate, insuffcien info.