My friend Joel has two children. In the following, you may assume that genders a

Question

My friend Joel has two children. In the following, you may assume that genders are equally likely, so are the 7 days of the week and the two are independent. Suppose I know that the elder child is female and born on Monday. What would the (conditional) probability be that both children are female? Suppose I only know that at least one of the children is female. What would the (conditional) probability be that both are female? Suppose I know that at least one of the children is female and born on Monday. Now what would the (conditional) probability be that both are female?

Explanation / Answer

A) P(2 females) = (1/2)x(1/2) = 1/4

P(elder female) = 1/2

P(2 females | elder female) = (1/4)/(1/2) = 1/2

B) P(at least one female) = 1 - P(both males)

= 1-1/4 = 3/4

P(both female | at least one female) = (1/4)/(3/4) = 1/3

C) Since the day of birth is independent, the probability wont change according to it. So, P(both female | at leat one is female and is born on monday) = 1/3

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