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

Answer:

0.762

Step-by-step 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

$x+4x=1$

$5x=1$

$x=\frac{1}{5}$

Hence, $P(E_1)=\frac{4}{5},P(E_2)=\frac{1}{5]$

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 $P(E_1/A)$

$P(E_1/A)=\frac{P(E_1)\cdot P(A/E_1)}{P(E_1)\cdot P(A/E_1)+P(E_2)\cdot P(A/E_2)}$

$P(E_1/A)=\frac{\frac{4}{5}\times 0.034}{\frac{4}{5}\times 0.034+\frac{1}{5}\times 0.034}$

$P(E_1/A)=\frac{0.0272}{0.0357}$

$P(E_1/A)=0.762$

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