00:01
In this question, we are given the following probabilities.
00:05
We are told that 95 % of highly successful products received good reviews.
00:11
So that's the probability of a good review, given that it turns out to be a highly successful product, is 0 .95.
00:19
60 % of moderately successful products had received good reviews, and 10 % of poor products received good reviews.
00:30
Furthermore, we are told that 40 % of products are highly successful, 35 % are moderately successful, and 25 % are poor.
00:40
For part a, we are asked for the probability that a product attains a good review.
00:47
So here we can use the law of total probability.
00:53
There are three ways to receive a good review.
00:58
It can be a highly successful product and receive a good review, or it can be a more moderately successful product and receive a good review.
01:25
I'm just going to write mod for moderately.
01:29
Or it can be a poor product and receive a good review.
02:07
And this comes out to a probability of 0 .615.
02:15
And then for b, we are asked, if a product attains a good review, what is the probability that it will be a highly successful product? so this is the probability that it's highly successful given that it attained a good review.
02:41
And for this situation, we can use bases theorem to solve this problem.
02:50
Bases theorem basically says that the probability of b given a is equal to the probability of a given b times the probability of b over the probability of a.
03:09
So for this situation, this is equal to the probability of good given highly times the probability that the product is highly successful, divided by the probability of a good product, of a good review...