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# Three cards are drawn successively, without replacement from a pack of 52 well shuffled cards. What is the probability the first two cards are kings and third card drawn is an ace?

Answer :

There are 52 cards in a deck. Let A be the event that first card drawn is a king. There are 4 hearts in the pack. Hence, the probability of the first card is a king is

Let B be the event that second card is also a king without replacement. Then there are 3 king cards out of 51 cards in the pack as the cards are not replaced. Therefore, the probability of the second card is a red is

Let C be the event that third card is an ace card without replacement. Then there are 4 ace cards out of 50 cards in the pack as the cards are not replaced. Therefore, the probability of the third card is an ace card is

Then the probabilities of getting first two cards are kings and third card drawn is an ace without replacement is

The probability that first two cards are kings and third card drawn is an ace without replacement is

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