Question

Factories A, B and C produce computers. Factory A produces 2 times as many computers as factory C, and factory B produces 7 times as many computers as factory C. The probability that a computer produced by factory A is defective is 0.035, the probability that a computer produced by factory B is defective is 0.048, and the probability that a computer produced by factory C is defective is 0.046. 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:0.154

Step-by-step explanation:

Given

Let factory A produces 2c unit

B produces  7c units

C produces c units

Probability a computer is chosen from A is $\frac{2}{10}$

$From B=\frac{7}{10}$

$from C=\frac{1}{10}$

Probability Of a defective computer  $=\frac{2}{10}\times 0.035+\frac{7}{10}\times 0.048+\frac{1}{10}\times 0.046=0.0452$

Probability that it came from factory A $=\frac{\frac{2}{10}\times 0.035}{\frac{2}{10}\times 0.035+\frac{7}{10}\times 0.048+\frac{1}{10}\times 0.046}=0.154$