Question

Write the sample space for the number of boys and the number of girls in a family with exactly three children. Are the outcomes equally likely?A.{3 girls, 2 boys and a girl, 1 boy and 2 girls, 3 girls}; The outcomes are equally likely.B.{3 boys, 2 girls and a boy, 2 boys and a girl, 3 girls}; The outcomes are equally likely.C.{3 boys, 2 boys and a girl, 1 boy and 2 girls, 3 girls}; The outcomes are not equally likely.D.{3 girls, 2 boys and a girl, 1 boy and 2 girls, 3 girls}; The outcomes are not equally likely.

Answer 1

The sample space for the number of boys, and number of girls in a family with exactly three children is

S = {GGG, GGB, GBG, GBB, BGG, BGB, BBG, BBB}

These are

GGG/BBB = three girls / three boys with a probability of 1/8.

GGB, GBG, BGG = two girls, and one boy, with a probability of 3/8

GBB, BGB, BBG = two boys, and one girl with a probability of 3/8

Summarizing, the outcomes are

{3 boys, 2 boys and 1 girl, 1 boy and 2 girls, 3 girls}; The outcomes are not equally likely.