Question

a couple decides to have children until they have one boy and one girl, but they will not have more than three children. choose the correct sample space for this random experiment.

s = {ggg, ggb, gbg, gbb, bbb, bbg, bgb, bgg}
s = {ggg, ggb, bbb, bgg}
s = {gb, bg, bbg, ggb}
s = {gb, bg, bbg, ggb, bbb, ggg}

Explanation:

Step1: Analyze the conditions

The couple stops when they have one boy and one girl or after having 3 children.

Step2: List the possible cases

• Case 1: First - born is a girl and second - born is a boy (GB).
• Case 2: First - born is a boy and second - born is a girl (BG).
• Case 3: First two are boys and third is a girl (BBG).
• Case 4: First two are girls and third is a boy (GGB).
• Case 5: All three are boys (BBB).
• Case 6: All three are girls (GGG).

Answer:

S = {GB, BG, BBG, GGB, BBB, GGG}