Question

given, set A={children of both sexes}, B={at most one boy}, if a family have two children then show that the sets are dependent events

Answer 1

work so far: please check
Universal set = { MM, MF, FM, FF} now, A = {MF, FM} and B = { MF, FM, FF} P(A) = 2/4 , P(B) = 3/4
P ( A intersect B ) = P ( A) = 2/4 because A intersect B is A
so we have P(B|A) = P(A&B) / P(A) = (2/4 ) / (2/4) and P(B) = 3/4, so A,B are not independent

Answer 2

maybe even easier to think that
\[B^c\] means no boys, and if that is the case then then
\[P(A|B^c)=0\]

Answer 3

that is incorrect, B ' is { MM}

Answer 4

youre doing this all wrong, -sighs-