00:01
So let's say here that the probability or the percentage of all customers that will return to the same grocery store is 75%, so we can write as well as 0 .75 as a proportion.
00:16
Considering this information, suppose that we have seven customers here.
00:22
They were collected at random.
00:26
So if for the first item, we want to compute what is the probability? that exactly five customers will return.
00:36
And i'm expressing x as the number of customers that return.
00:42
So in this case here, we should compute this probability.
00:48
So the thing that we should use here to compute this is basically the binomal distribution.
00:57
So because we accounted the number of successes, the success here is that if the customer returned to the grocery, in this case, should return to the grocery.
01:08
So the success is that these customers that return to the grocery store.
01:13
So we are counting the number of successes, and we know that 75 % of them, or the probability that a customer will return to the store is 0 .75.
01:26
5.
01:27
This means that this is a binomial experiment.
01:32
So basically here, we're going to use the binomial distribution to compute this probability.
01:40
In the binomial distribution here, we use that the probability of x being equals to a little x is given by a combination because we are selecting people.
01:52
And there are different ways, different, like, there is like a different ways to select these people.
01:58
So basically here, we are going to put n, which is the total number of customers selected, which in our case is seven.
02:08
And we are saying the x is the number of customers out of this seven that returned to the grocery store.
02:19
Then we should put here the probability that eight costs over will.
02:22
Return to the store, which is 0 .75.
02:26
Power of x, because we have the x customers return to the store.
02:34
And the number of customers that did not return, so this he expressed like the probability of not return to the store, is the number of customers in total minus the ones that returned.
02:48
So this means that this here represents the number of customers that did not return to the store.
02:53
So considering this formula, we can find this probability as 7 .5, 0 .755, and 0 .252.
03:07
So basically, if you use like a calculator to find this probability, you're going to get here that this probability is 0 .3115.
03:22
Now for the second item, we are interested in the probability, the less than or fewer than six will return.
03:36
So this means, and the question specifies that we should use the complement rule.
03:42
So this means that the complement rule basically means that we can compute this probability as 1 minus the complement.
03:50
And the complement of like less than six return to the store is the same as like the opposite of this.
04:00
So the opposite of this here will be the number of customers here that return to the store should be greater or equal than six.
04:11
So this is the opposite...