00:01
In order to answer this question, let's talk about probabilities.
00:03
It says, assuming a one -to -one -beard ratio that loss of probability predict that half, that children in a family will be boys and half will be girls.
00:12
And this is true because in each pregnancy, there are 50 % chances to get a son and 50 % chances to get a daughter.
00:23
Okay, so this is the probability for each of this or for each pregnancy.
00:28
It says, what is the probability? that this expected outcome would occur in a family of four children.
00:35
So the question here is that you want a family of four children.
00:39
So you have one, two, three, and four.
00:43
Okay.
00:44
And you want that half of them are girls and half of them are boys.
00:49
So you want, for example, something like this.
00:52
Song, son, daughter and daughter.
00:55
This is one possibility, but you also want, or it can also be something like this.
01:02
Son, daughter, son, and daughter.
01:06
Like this.
01:06
This is a different combination, but it is still two sons and two daughters.
01:12
Or it can be something like this, daughter, daughter, song, and son.
01:15
So there are many combinations.
01:17
So in this case, you can find the different combinations because there are only a few combinations here.
01:23
But when you have many different objects in the set, for example, instead of four, a family of four, you can have a family of 20.
01:33
You're not going to be finding all the different combinations like this in this form.
01:36
Okay, you're going to require a formula that is like this.
01:43
This is factorial divided by r factorial, multiply in minus r factorial, okay? where this c is the number of combinations.
01:55
It means the number of combinations like this, like i did here.
01:58
For example, you have two, only two, but you have many others.
02:01
I'm going to find how many of how many combinations, different combinations you can find with this information.
02:10
In is a total number of objects in the set.
02:13
So in this case, you have four, because you have four members in that in this family.
02:19
So you have four factorial divided by r, factored, and r is a number of choosing objects from the set.
02:25
So you want two daughters and you want also two songs.
02:29
So you have here 2 factorial.
02:33
And then you have n minus r factorial.
02:36
N minus r is practically 4 minus 2 that is also 2 factorial, okay? like this.
02:43
So 4 factorial is the same as 4 multiplied by 3, multiply by 2, and multiply by 1.
02:51
And you divide this by 2 multiplied by 1, that is 2 factorial, and also 2 multiply by 1 that is for this number here.
03:00
So you can simplify this in you're going to get a number of six.
03:08
It means that with this information you have six possibilities.
03:12
And in this case, we can find all those six combinations.
03:17
For example, again, let's start with this.
03:24
Son, son, daughter, and daughter.
03:27
Another possibility would be son, daughter, son, daughter.
03:32
Another possibility can be song, daughter, daughter, son.
03:38
Another possibility can be daughter, daughter, son and song.
03:43
Then another possibility can be daughter, son, daughter, and son.
03:48
And the last possibility would be daughter, son, son, and daughter.
03:53
Okay, so as you can see here, you have one, two, three, four, five, and six possibilities as well as we found that here.
04:01
So you have six different combinations...
