Indicated Probability

Question

A couple plans to have 3 children. If genders are independent and there is a 69% chance of a child being a girl find the probability they have 2 girl

Answer 1

Hi Rebekah,

 

The probability problem can be treated as a binomial distribution problem with the following given items

n=3

c=combination

p=0.69...probability of getting a girl

q=1-p=1-0.69=0.31...probability of having a girl

x= 2...number of girls we are interested in

p(x=2)=?

 

using the binomial formula, p(X=x) = ncx*p^x*q^n-x

                                        p(x=2) = 3c2*.69^2*0.31^3-2

                                                   = 3*.4761*.31

                                                   = 0.442773

                                                   = 44.28%

 

Therefore, the couple has a 44.28% chance of getting 2 daughters and a son if they plan to have 3 children

 

Thanks,

A.