00:01
In this problem, we are given information about the tv sales in an electronic store in the last six months.
00:09
Now, what we need to determine is that if a customer is randomly selected from all of those who bought a tv from the store, and what is the probability that the customer purchased an extended warranty? now, considering the information given in the question, let us first of all define a few events.
00:25
Let b1 be the event that a customer purchased the brand 1 model tv.
00:29
Let b2 be the event that a customer purchased the brand 2 model.
00:34
And let e be the event that a customer purchased an extended warranty.
00:40
Then we have been asked to determine the probability of e, the probability that a customer purchased an extended warranty.
00:47
And to find this, we will use the law of total probability.
00:58
Now, to use the law of total probability, we need a set of mutually exclusive and exhaustive events.
01:03
In this case, we'll use the events b1 and b2.
01:06
They are mutually exclusive because each customer buys one tv and that tv cannot be both brand one and brand two at the same time.
01:15
And they are exhaustive because we only have these two brands.
01:19
There are no other brands.
01:20
So using those two events b1 and b2 and using the law of total probability, p of e will be equal to p of b1 times p of e given b1 plus p of b2, times p of e given b2.
01:39
So consider p of b1.
01:40
That is the probability that a customer purchases the brand one model tv.
01:44
And that is given in the question to be 70%...