Question

You select a family with three children. It M represents a male child, and F represents a female child, the set of equally likely outcomes for the children's genders is (MMM, MIMF MFM, MFF, FMM, FMF, FFM, FFF ) Find the probability of selecting a family with fewer than 5 male children P(fewer than 5 male children) Type an integer or a simplified fraction.)

Answer 1

Answer with explanation:

→If a Family has five children, then Total likely outcome can be represented as:

Five Male =1

Five Female =1

4 Male +1 Female =4

4 Female +1 Male =4

3 Male +2 Female =10

3 Female +2 Male =10

Total Possible Outcome

 =1+1+4+4+10+10

or

   =2×2×2×2×2

     =32

,i.e either a children can be a male or female.

→If all the five childrens are male , then in the family number of children fewer than 5 male children =32-1=31

→Probability of an Event

         $=\frac{\text{Total favorable Outcome}}{\text{Total Possible Outcome}}$                    

→→Probability of selecting a family with fewer than 5 male children

       $=\frac{31}{32}$