Question

A VCR manufacturer receives 70% of his parts from factory F1 and the rest from factory F2. Suppose that 3% of the output from F1 are defective while only 2% of the output from F2 are defective. a. What is the probability that a received part is defective? b. If a randomly chosen part is defective, what is the probability it came from factory F1?

Answer 1

Answer:

See the explanation.

Step-by-step explanation:

Lets take 1000 output in total.

From these 1000 outputs, 700 are from F1 and 300 are from F2.

Defective from F1 is $\frac{700\times3}{100} = 21$ and defective from F2 is $\frac{300\times2}{100} = 6$.

a.

Total received part is 1000.

Total defectives are (21+6) = 27.

The probability of a received part being defective is $\frac{27}{1000}$.

b.

The probability of the randomly chosen defective part from F1 is $\frac{21}{27} = \frac{7}{9}$.