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.

rounding to the nearest thousandth would be 452,000

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.