Question

Factories A and B produce computers. Factory A produces 4 times as many computers as factory B. The probability that an item produced by factory A is defective is 0.034 and the probability that an item produced by factory B is defective is 0.034. A computer is selected at random and it is found to be defective. What is the probability it came from factory A?

Answer 1

0.762

Explanation:

We are given that

Factory A produces 4 times as many computers as factory B

Let
`E_1 and E_2` be the event denotes computers produced by factory by A and factory by B.

Let
`P(E_2)=x`

Then
`P(E_1)=4x`

Sum of all probabilities=1

`x+4x=1`

`5x=1`

`x=(1)/(5)`

Hence,

Let A denotes the event that an item is defective.

`P(A/E_1)=0.034,P(A/E_2)=0.034`

We have to calculate
`P(E_1/A)`

`P(E_1/A)=(P(E_1)\cdot P(A/E_1))/(P(E_1)\cdot P(A/E_1)+P(E_2)\cdot P(A/E_2))`

`P(E_1/A)=((4)/(5)* 0.034)/((4)/(5)* 0.034+(1)/(5)* 0.034)`

`P(E_1/A)=(0.0272)/(0.0357)`

`P(E_1/A)=0.762`

Hence, the probability that the item produced by factory A and it is found to be defective=0.762