Question
Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability that first two cards are kings and the third card drawn is an ace?
Solution
Let K denote the event that the card drawn is king and A be the event that the card drawn is an ace.
Now,
Also, P(K | K) is the probability of second king with the condition that one king has already been drawn. Now there are three kings in (52 - 1) = 51 cards.
Again, P(A | KK) is the probability of third drawn card to be an ace, with the condition that two kings have already been drawn. Now, there arc four aces in remaining 50 cards.
By multiplication law of probability, we have
Now,
Also, P(K | K) is the probability of second king with the condition that one king has already been drawn. Now there are three kings in (52 - 1) = 51 cards.
Again, P(A | KK) is the probability of third drawn card to be an ace, with the condition that two kings have already been drawn. Now, there arc four aces in remaining 50 cards.
By multiplication law of probability, we have
