00:01
A family has three children.
00:05
Assuming that the probability to have a boy is the same probability to have a girl, find the remaining probabilities.
00:13
Probability a, that all children are girls.
00:16
So let's start the information that we know.
00:18
The probability to have a girl is the same probability to have a boy.
00:21
That is equal to 1 half, equal probabilities.
00:27
The probability to have all girls will correspond to the probability to have a first girl time is probably have a second girl.
00:36
Time is probably have a third girl.
00:39
Yielding 1 over 8, because order is not important in this case.
00:42
These are all independent events.
00:44
And these are all independent events.
00:50
Order is probably to have at least one boy.
00:53
So there's two ways to compute this.
00:55
One is to use a bit more reasoning.
00:58
And one is to just enumerate all the possibilities.
01:01
So let's go through both possibilities, both reasonings.
01:05
So let's go through all the different ways we can have at least one boy.
01:08
So perhaps the first child is a boy, and there are remaining two are girls.
01:16
That's one way to have at least one boy.
01:21
Perhaps the first one is a girl, the second is a boy, and the last is a girl.
01:28
And then maybe the last one is a boy.
01:31
So this is the probability to have one boy.
01:36
But here we have at least one boy, so what about the probabilities to have two boys? well, perhaps the first two are a boy and the last is a girl.
01:50
The first is a girl and the last two are boys.
01:57
And the middle child is a girl, so only the first and last are boys...