Question 1206803: An automobile manufacturer has three factory A,B and C.They produce 50%,30% and 20% respectively of the specific model of car.30% of those produced in factory A are white,40% produced in factory B are white and 25% produced in factory C are white.
a.if an automobile produced by the company is selected at random,find the probability that is white.
B.Given that an automobile selected at random is white ,find the probability that it come form factory B.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! factory A produces 50% of all cars = .5
factory B produces 30% of all cars = .3
factory C produces 20% of all cars = .2
30% of cars produced in factory A are white = .3 * .5 = .15.
this means that 15% of all cars produced are white and produced in factory A.
40% of cars produced in factory B are white = .4 * .3 = .12.
this means that 12% of all cars produced are white and produced in factory B.
25% of cars produced in factory C are white = .25 * .2 = .05.
this means that 5% of all cars produced are white and produced in factory C.
the probability that the car is white is equal to .15 + .12 + .05 = .32.
this means that the probability that the car is white is 32%, regardless of which of the 3 factories produced it.
let D = the probability that the car is white = .32
let E = the probability that the car is produced in factory B = .3
let DE = the probability that the car is white and produced in factory B = .12
the probability that the car is produced in factory B given that the car is white is given by the equation p(E given D) = p(DE) / p(D) = .12 / .32 = .375.
to see how this works, take some fictitious number of cars produced and work it through, as i did in the following table that assumes 1000 cars were built in total.
50% of the cars were built in factory A = .5 * 1000 = 500
30% of the cars were built in factory B = .3 * 1000 = 300
20% of the cars were built in factory C = .2 * 1000 = 200
30% of the cars built in factory A were white = .3 * 500 = 150
40% of the cars built in factory B were white = .4 * 300 = 120
25% of the cars built in factory C were white = .25 * 200 = 50
total cars built were 1000
total white cars built were 320.
total cars built in factory B were 300.
total white cars built in factory B were 120.
number of all cars built in factory B divided by total number of all cars built = 300 / 1000 = .3.
number of all white cars built in factory B divided by total number of all cars built = 120 / 1000 = .12.
number of all white cars built in factory B divided by total number of all white cars built = 120 / 320 = .375.
your solutions are:
A. if an automobile produced by the company is selected at random, find the probability that is white.
that probability is .32 = 32%.
B. given that an automobile selected at random is white, find the probability that it came from factory B.
that probability is .375 = 37.5%.
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