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Two cards are drawn without replacement from a pack of 52 cards. Find the probability that the first is a king and the second is an ace |
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Answer» Total number of all favorable cases is n(S) = 52 Let A be the event that first card drawn is a king. There are four kings in the pack. Hence, the probability of the first card is a king is P(A) = \(\cfrac{4}{52}\) Let B be the event that second card is an ace without replacement. Then there are 4 aces in the pack as the cards are not replaced. Therefore, the probability of the second card is an ace is P(B|A) = \(\cfrac{4}{51}\) Then the probability of getting first is a king and the second is an ace without replacement is = P(A)P(B|A) ⇒ \(\cfrac{4}{52}\times\cfrac{4}{51}\) (as there are 4 kings out of 52 cards in first draw, and 4 aces out of 51 cards in the second draw as the cards are not replaced) ⇒ \(\cfrac{4}{663}\) The probability that first is a king and the second is an ace without replacement is \(\cfrac{4}{663}\) |
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