A family has two children. find the probability that both the children are girls given that at least
one of them is a girl? Choose the most appropriate option.
A) 1 / 5 B) 1 / 3 C) 3 / 7 D) 2 / 7 E) 3 / 7

Rationale: let b stand for boy and g for girl . the sample space of the experiment is s = { ( g , g ) , ( g , b ) , ( b , g ) , ( b , b ) } let e and f denote the following events : e : ‘ both the children are girls ’ f : ‘ at least one of the child is a girl ’ then e = { ( g , g ) } and f = { ( g , g ) , ( g , b ) , ( b , g ) } now e n f = { ( g , g ) } thus p ( f ) = 3 / 4 and p ( e n f ) = 1 / 4 therefore p ( e | f ) = p ( e ∩ f ) / p ( f ) = ( 1 / 4 ) / ( 3 / 4 ) = 1 / 3 b )
Answer: B