00:01
Assuming boys and girls are equally likely, and the couple already has three girls, what's the probability of the fourth child being a girl? okay, so the point of this question is that each child is an independent event.
00:14
The previous three children do not affect the probability of the fourth.
00:19
So the fourth is still 50 -50.
00:22
So it's a half.
00:28
Which brings us on to part two.
00:29
Probability of a baby being a girl.
00:32
So that's p equals 0 .463, which means probability of it being a boy, 1 minus p, is 0 .537.
00:44
There are five randomly selected berths.
00:47
What's the probability that at least one of them is a boy? so we have two outcomes and we have independent events.
00:53
So this is a binomial question.
00:59
And here, n equals five, because we have five events that we're looking at.
01:04
So the binomial formula is p equals n choose k, p to power of k, 1 minus p to power of n minus k.
01:16
So this is the event we're looking at happening k times.
01:20
This is the other event happening the rest of the time, and this is how many different ways you can put your events in order.
01:28
So we want at least one boy.
01:31
So the only event we don't want is no boys...