Question

Create a sample space for having four children. Then, find the probability that when a couple has four children, there are exactly two boys.

Answer 1

Solution:

Part a) Create a sample space for having four children.

4 Boys	3 Boys 1 Girl	2 Boys 2 Girls	1 Boy 3 Girls	4 Girls
BBBB	BBBG	BBGG	BGGG	GGGG
	BBGB	BGBG	GBGG
	BGBB	GBBG	GGBG
	GBBB	GBGB	GGGB
		GGBB
		BGGB

We can write collectively as follows:

S = { BBBB, BBBG, BBGB, BGBB,   GBBB, BBGG, BGBG, GBBG,   GBGB, GGBB, BGGB, BGGG,   GBGG, GGBG, GGGB, GGGG}

n = Total outcomes = 16

Part b)  find the probability that when a couple has four children, there are exactly two boys.

P( exactly two boys ) =.............?

exactly two boys = { BBGG, BGBG, GBBG,   GBGB, GGBB, BGGB }

m = Number of outcomes for exactly two boys = 6

Thus

P( exactly two boys ) = m / n

P( exactly two boys ) = 6 / 16

P( exactly two boys ) = 3 / 8

P( exactly two boys ) = 0.375