Question

If the part is inspected and found to be defective, what's the probability that it was produced by Machine C?

a) 10%
b) 30%
c) 40%
d) Not enough information provided

Answer 1

To find the probability that a defective part was produced by Machine C, we can use conditional probability. Using Bayes' theorem, we determine that without more information, we cannot calculate the exact probability.

Step-by-step explanation:

To find the probability that a defective part was produced by Machine C, we need to use conditional probability. Let's use the following variables:

D: Event that the part is defective

C: Event that the part was produced by Machine C

We are given:

P(C) = 0.2 (probability that a randomly selected part is produced by Machine C)

P(D|C) = 0.6 (probability that a part produced by Machine C is defective)

To find P(C|D), the probability that the part was produced by Machine C given that it is defective, we can use Bayes' theorem:

• P(C|D) = (P(D|C) * P(C)) / P(D)
• P(D) can be found using the law of total probability: P(D) = P(D|C) * P(C) + P(D|~C) * P(~C)
• Since we don't have the value of P(D|~C) or P(~C), we cannot determine the exact probability. Therefore, the answer is d) Not enough information provided.