00:01
In this problem, it is said that babies born are equally likely to be boys or girls.
00:05
We assume that a woman has six children, none of whom are twins, and we need to determine which of the given sequences is more likely.
00:13
Now, first of all, let us consider the probability of having a boy.
00:18
Since having boys and girls is equally likely, the probability of having a boy will be half.
00:24
And this will also be the probability of having a girl.
00:26
Now, if we consider the first sequence a, and note that the children, their gender, will be independent of each other, whether or not one child is a girl or a boy, does not affect whether or not the other children or girls or boys.
00:42
And because of that, we can use the multiplication rule of probability for independent events.
00:47
And according to that, the probability of sequence a, that is the probability of having a girl and then a girl and so on, will just be the probability of having a girl times the probability.
00:56
Of having a girl times the probability of having a girl and so on.
01:02
So the probability of having a girl is half and we have six d's in the sequence.
01:07
So we have half to the power of six...