Question

A car manufacturing factory has two plants, X and Y. Plant X manufactures 70% of cars and plant Y manufactures 30%. 80% of the cars at plant X and 90% of the cars at plant Y are rated of standard quality. A car is chosen at random and is found to be of standard quality. What is the probability that it has come from plant X?

Answer 1

Let E be the event that the car is of standard quality.

Let B₁ and B₂ be the events that the car is manufactured in plants X and Y, respectively.

Now P(B₁) = `70/100 = 7/10`

P(B₂) = `30/100 = 3/10`

P(E|B₁) = Probability that a standard quality car is manufactured in plant

= `80/100 = 8/10`

P(E|B₂) = `90/100 = 9/10`

P(B₁|E) = Probability that a standard quality car has come from plant X

= `("P"("B"_1) xx "P"("E"|"B"_2))/("P"("B"_1) * "P"("E"|"B"_1) + "P"("B"_2) * "P"("E"|"B"_2))`

= `(7/10 xx 8/10)/(7/10 xx 8/10 + 3/10 xx 9/10)`

= `56/83`

Hence the required probability is `56/83`.