Acertain firm has plants a, b, and c producing respectively 35%, 15%, and 50% of the total output. the probabilities of a non-defective product are, respectively, 0.75, 0.95, and 0.85. a customer receives a defective product. what is the probability that it came from plant c?

There is a 44.12% probability that the defective product came from C.

Step-by-step explanation:

This can be formulated as the following problem:

What is the probability of B happening, knowing that A has happened.

It can be calculated by the following formula

Where P(B) is the probability of B happening, P(A/B) is the probability of A happening knowing that B happened and P(A) is the probability of A happening.

-In your problem, we have:

P(A) is the probability of the customer receiving a defective product. For this probability, we have:

In which is the probability that the defective product was chosen from plant A(we have to consider the probability of plant A being chosen). So:

is the probability that the defective product was chosen from plant B(we have to consider the probability of plant B being chosen). So:

is the probability that the defective product was chosen from plant B(we have to consider the probability of plant B being chosen). So:

So

P(B) is the probability the product chosen being C, that is 50% = 0.5.

P(A/B) is the probability of the product being defective, knowing that the plant chosen was C. So P(A/B) = 0.15.

So, the probability that the defective piece came from C is:

There is a 44.12% probability that the defective product came from C.