00:01
Okay, in this question we are asked or told in a certain country, the true probability of a baby being born a boy is 0 .515.
00:11
Among the next eight randomly selected births in the country, what is the probability that at least one of them is a girl? okay, so the trick to this question is to understand what's going on here.
00:24
At least one girl means we could have one birth girl out of eight, two birth girls out of eight, three birth, four birth, five, all the way up to all eight births being girls would be okay or favorable for this probability.
00:42
Now, if you think about that, that's a lot of probabilities to calculate.
00:45
We would have to calculate the probability of one girl and then add that to the probability of two girls.
00:51
And when you start to get into that, it's going to be messy because that first girl, the one girl could have been born in any of those eight positions.
01:01
The two girls could be born in any of those eight positions, say like first and last or first and second.
01:08
Each one of those would carry their own probabilities.
01:12
So this is almost like an overwhelming question if you look at it that way.
01:17
So you need to take a step back and think about, okay, if we want at least one girl, the compliment.
01:26
And that's the key word to this.
01:28
The complement to that situation would be no girls born.
01:33
So no girls being born would represent the situation where, you know, we have eight births and absolutely no girls.
01:44
Any other probability or any other situation that occurs would have to have a girl in it.
01:50
So i have set up the probability of at least one girl.
01:54
And the way you find a complement is you take one minus.
01:58
Whatever you're looking for is the compliment here.
02:01
My compliment would be the probability of all boys...