00:01
We are given in the question that a family has four children, that is n is equal to four.
00:16
And there are 50 % of chance that the child is female.
00:21
So, p is 0 .5.
00:25
Now in part a, we have to find the probabilities associated with number of daughters.
00:32
So, let us consider x with a number of daughters.
00:36
Number of daughters in family.
00:49
So, x will be a binomial where n is equal to 4 and p is 0 .5.
01:03
So we know by binomial that royalty of x is equal to x is given by ncx multiply p raised to power x, multiply 1 minus p, raise to power x, multiply 1 minus p, power n minus x.
01:24
So putting the values as royalty of x is equal to 0, that is no daughter.
01:31
It will be 4c0, multiply p raised to power 0, that is 0 .5 raise to power 0, multiply 1 minus 0 .5 raise to power 0.
01:45
So it will be 4 factorial, divide 0 factorial, multiply 4 factorial, multiply 0 .5 raise to power 4, which will be 0 .0625.
02:15
As we know that ncr is equal to n factorial, divide r factorial, multiply n minus r factorial.
02:25
So this is the priority that the family has no daughter.
02:31
Now the priority that family has one daughter, it will be 4 c1, multiply 0 .5 raise to power 1, multiply 1 minus 0 .5 raise to power 3, which will be 4 multiply 0 .5 which is the priority that family has one daughter.
03:05
Now let us find the priority that family has two daughters.
03:11
So, priority that x is equal to 2...