Question

In a bolt factory, machines 1,2, and 3 respectively produce 20%, 30% and 50% of the total output. of their respective outputs 5%, 3%, and 2% are defective. a bolt is selected at random.

a. What is the probability that is defective?
b. Given that is defective, what is the probability that it was made by machine 1?

Answer 1

a. 1/10 or 10%

b. 1/2 or 50%

Explanation:

Since the combination of machines 1, 2 and 3 produce 100% of the total output when added together, then the probability of choosing a bolt at random that is defective is: 5 + 2 + 3 = 10% out of 100% or 10/100, which is 1/10 or 10%.

If the bolt that is choosen at random is defective, than the probability that it came from machine 1 is 5/10 or 1/2 which is also 50%.