Question

You select a family with three children. If M represents a male​ child, and F represents a female​ child, the set of equally likely outcomes for the​ children's genders is​ { MMM,​ MMF, FFM,​ MFF, FFM,​ FMF, FFM, FFF​ }. Find the probability of selecting a family with nothing 6 male children.

Answer 1

Answer:

1/8

Step-by-step explanation:

This is actually pretty easy.

First, you have the sample of the children.

You know that the family with 3 children, can only have the following children:

MMM: all males

MMF: 2 males, 1 female

MFF: 1 male, 2 females

MFM: 2 males, 1 female (different order)

FMM: 1 female, 2 males

FFM: 2 females, 1 male

FMF: 2 females, 1 male

FFF: 3 females

If you count all of these possibilities, we have 8 possible cases of family with the childrens.

In only one of them, we have only females and no males, which is the last one, all 3 females.

Therefore, the probability to select a family with no male, is only 1/8.