a mom wants to have exactly 2 daughters. Assuming that boy and girl babies are equally likely, find the probability of success if she has a total of 2 children

Question

a mom wants to have exactly 2 daughters. Assuming that boy and girl babies are equally likely, find the probability of success if she has a total of 2 children

or

 the probability of success if she has a total of 3 children.

Answer 1

For this question we have to use the binomial equation:

(nCr)p^rq^n-r

 

where 

nCr is the combination equation n!/(n-r)!r!

n=number of trials

r=number of successes

p=probability of success

q=probability of failure (1-p)

 

If the mother has only two children, the probability of getting exactly two successes (daughters) is:

(₂C₂)(.5)²(.5)^2-2

(1)(.5)²(1) = .25

 

If the mother has three children, the probability of getting exactly two successes is:

(₃C₂)(.5)²(.5)^3-2

(3)(.25)(.5) = .375