# An auto manufacturer has three factories A B and C which produce 50%, 25%, and 25%, respectively, of a particular auto. Seventy percent of the autos produced in factory A are passenger autos, 25%...

An auto manufacturer has three factories A B and C which produce 50%, 25%,

and 25%, respectively, of a particular auto. Seventy percent of the autos produced

in factory A are passenger autos, 25% of those produced in factory B are

passenger autos, and 25% of the autos produced in factory C are passenger autos.

If an auto produced by the manufacturer is selected at random, calculate the

probability the auto will be a passenger auto.

tjbrewer | Certified Educator

Factory A produces 50% of all models, and 70% of the 50% are passenger models.

Factory B produces 25% of all models, and 25% of the 25% are passenger models.

Factory C produces 25% of all models, and 25% of the 25% are passenger models.

Let's assume that the producer makes 100 cars combined.  50 of them are from Factory A, and 70% of the 50 are passenger models.  70% of 50 is `.70xx50=35` So factory A produces 35 passenger cars.  25 of the autos are from Factory B, and 25% of the 25 are passenger models.  25% of 25 is `.25*25=6.25` rounding to the nearest whole, Factory B produces 6 Passenger cars.  Factory C's calculations are the same as Factory B.

Factories A, B and C produce 35, 6, and 6 passenger cars respectively, that's a combined 47 passenger cars out of every 100 cars the manufacturer makes.  If a car is chosen at random, the probability is 47 out of 100, or 47% that the car will be a passenger car.