Boys and Girls

In a family of 8 children, what is the probability of the following gender birth:

1-That 4 are boys and 4 girls

8C4 * 0.5^4 * 0.5*^4 = 4C4 * 0.5^8

 

 

2-That 3 are boys and 5 girls, or 3 girls and 5 boys(which is the same probability)

8C3 * 0.5^8

 

3-That 2 are boys and 6 girls, or 2 girls and 6 boys(,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)

8C2 * 0.5^8

 

4-That 1 is a boy and 7 are girls, or 1 girl and 7 boys(,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)

8C1 * 0.5^8

 

5-That all 8 are girls, or all 8 are boys(,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)

0.5^8

In a family of 8 children, what is the probability of the following gender birth:

1-That 4 are boys and 4 girls

2-That 3 are boys and 5 girls, or 3 girls and 5 boys(which is the same probability)

3-That 2 are boys and 6 girls, or 2 girls and 6 boys(,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)

4-That 1 is a boy and 7 are girls, or 1 girl and 7 boys(,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)

5-That all 8 are girls, or all 8 are boys(,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,)

 

HERE WE GO:

1- [8!/(4!*4!)] / 2^8 X 100=27.34%

2- [8!/(3!*5!)] / 2^8 X 100=21.875%

3- [8!/(2!*6!)] / 2^8 X 100=10.9375%

4- [8!/(1!*7!)] / 2^8 X 100=3.125%

5- [8!/(0!*8!)] / 2^8 X 100=.390625%