00:01
In this problem, we have been asked to determine the probability of obtaining two boys out of five children, with the probability of a boy is 0 .51 at each birth, and the sexes of the successive children are considered to be independent random variables.
00:16
So, in this case, if we consider x to be the random variable, which represents the number of boys, then this random variable x, this will follow.
00:30
A binomial distribution.
00:37
Now we can say that it follows a binomial distribution because it satisfies all four conditions required for the binomial distribution.
00:45
The first condition is that there are a fixed number of trials.
00:48
Now here we need to find the probability of obtaining two boys out of five children.
00:53
So the number of trials is five.
00:55
So we can say that the number of trials n is equal to five.
00:58
Now the second condition is that each trial needs to be independent.
01:02
Now, we it said that the sexes of the successive children are considered to be independent random variables.
01:07
So this condition is satisfied as well.
01:09
The third condition is that there should be exactly two outcomes.
01:13
One is a success and the other is a failure.
01:15
In this case, we will consider a boy to be a success and a girl to be a failure.
01:21
So there are just two outcomes and this condition is satisfied...