Three machines turn out all the products in a factory, with the first machine producing 40% of the products, the second machine 35%, and the third machine 25%. The first machine produces defective products 12% of the time, the second machine 3% of the time and the third machine 15% of the time. What is the probability that a non-defective product came from the second machine?
To find the probability that a non-defective product came from the second machine, we need to multiply the probability of each event happening and then sum up the results.
Let's break it down step by step:
1. Calculate the probability that a product is produced by the second machine:
Probability of second machine = 35% = 0.35
2. Calculate the probability that a product is non-defective if produced by the second machine:
Probability of non-defective product from second machine = 100% - 3% (defective) = 97% = 0.97
3. Calculate the overall probability that a non-defective product came from the second machine:
Probability = Probability of second machine * Probability of non-defective product from second machine
= 0.35 * 0.97
= 0.3395
So, the probability that a non-defective product came from the second machine is approximately 0.3395 or 33.95%.