A single card is drawn from a standard deck of playing cards. What is the probability that the card is a queen provided that a face card is drawn from the deck of cards?
Answer
face cards are King Queen and jack
P(Q|F) = P(Q∩F)/P(F) = P(Q)/P(F) = (4/52)/(12/52) = 4/12 = 1/3
as P(Q∩F) = P(Q) , as Queen is already a face card.
Supposedly a friend of yours has 2 children and at least one of them is a boy. What is the probability that the other is also a boy?
Answer
P(B)=P(G)=1/2
P(BB)=P(BG)=P(GB)=P(GG)=1/4
Probability that the other one is a boy = P(B)=1/2
Probability that the other is also a boy, given at least one of them is a boy=P(BB)/[P(BB)+P(BG)+P(GB)]
=(1/4)/(3/4) =1/3
