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?
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%.
