Question

In families with four children, you're interested in the probabilities for the different possible numbers of girls in a family. Use theoretical probability (assume girls and boys are equally alike),compile a five -column table with the headings, O through 4, for the five possible numbers of girl children in a four child family. Then using G for girls and B for Boys, list under each heading the various birth order ways of achieving that number of girls in a family. Use table to calculate the following probabilities:

1. The probability of 1 girl.

2. The probability of 2 girls.

3. The probability of 4 girls.

4. The probability the third child born is a girl.

The probability of 4 girls

Answer 1

Let us construct the table

0 girl	1 girl	2girls	3girls	4girls
BBBB	GBBB	GGBB	GGGB	GGGG
	BGBB	GBGB	GGBG
	BBGB	GBBG	GBGG
	BBBG	BBGG	BGGG
		BGBG
		BGGB

The column heads  in the above table represent number of girls . We can see from the above table , there are 16 all possible cases .

1) total number of cases = 16

favorable number of cases for 1 girl = 4

Probability of an event = favorable number of cases / total number of cases

Probability of 1 girl = 4/16 = 0.25

2) total number of cases = 16

favorable number of cases for 2 girls = 6

Probability of 2 girls = 6/16 = 0.375

3) total number of cases = 16

favorable number of cases for 4 girls = 1

Probability of 4 girls = 1/16 = 0.0625

4) From the table above , we select only those cells where third child is a girl

0	1	2	3	4
			GGGB	GGGG
		GBGB
	BBGB		GBGG
		BBGG	BGGG
		BGGB

total number of cases = 16

favorable number of cases =8

Probability that the third child born is a girl  = 8/16 = 0.5