00:01
In this problem, it is said that a research survey suggests that 27 % of adults regularly get news through social networking sites.
00:09
We need to find the probability that in a random sample of 10 people, at most one of them, get their news through social networking sites.
00:17
Now, let us consider x to be the random variable, which gives us the number of people in the sample who get their news through social networking sites.
00:25
In that case, this random variable x, this will follow a binomial distribution.
00:33
Now, the reason for that is that all four conditions for being a binomial distribution are satisfied.
00:40
Now, the first condition is that the number of trials n should be fixed.
00:44
In this case, there is a random sample of 10 people, so we can say that the number of trials n is equal to 10.
00:50
Now, the second condition for being a binomial distribution is that all the trials should be independent.
00:55
Now, in this case, whether or not one person regularly gets their news through social networking sites does not affect in any way or form whether or not any of the other adults get their news through social networking sites.
01:07
So that means that the trials are all independent.
01:09
So the second condition is satisfied.
01:12
Now, the third condition is that there should be exactly two outcomes, a success and a failure.
01:16
So in this case, a success will be that a person does get their news through social networking sites, and a failure will be that a person does not get.
01:25
The news through social networking sites.
01:27
This is because x is the random variable which counts the number of people who gets their news through social networking sites.
01:34
So success is getting news to social networking sites.
01:37
So that's the third condition.
01:39
And the fourth condition is that the probability of success p, this should be constant for each and every trial.
01:45
And it has said that 27 % of adults regularly get their news to social networking sites.
01:50
So this probability p, probability of success, will be 27 % or 27 by 100 or 0 .27 .27.
01:57
And this is constant for every single person.
02:00
So this is constant for every trial.
02:02
Thus all four conditions that the binomial distribution are satisfied.
02:06
Now let us consider the probability of failure q, that is 1 minus p or 1 minus 0 .27, which is 0 .73...