00:01
For this problem, we are told that a company ships out some electronic component from four locations, location 1, 2, 3, and 4.
00:11
We are also told that sourcing these products from each of the four locations is equally likely.
00:18
So that means the probability that it comes from location 1 is equal to the probability that it comes from 2, 3, and 4.
00:26
So each one has a probability of 1 4th.
00:28
We are also told the defect rate for components coming from location 1 is 5%.
00:37
It's 40 % from components coming from location 2, 10 % from location 3, and 10 % from location 4.
00:48
And so for the question, we are told that a component has come back on warranty.
00:53
So given that the return component is defective, what is the probability that it came from location 2? so stating this mathematically, what is the probability it came from location? location 2, given that the component is defective.
01:11
Now to solve this, we can use basa theorem, which basically states that the probability of b given a is equal to the probability of a given b times the probability of b divided by the probability of a.
01:34
So in our situation, this is equal to the probability of the component being defective, given that it came from location 2 times the probability of being from location 2...