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Three cards are drown 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 ? |
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Answer» The experiment is drawing three cards successively without replacement. Since, total numbers of kings are 4 in the pack of 52 cards. Therefore, the probability of getting king in first drawn is P(E1 ) = \(\frac{4}{52}\) = \(\frac{1}{13}\) . Since, the card king is not replaced after first draw, therefore, total numbers of 51 cards are left in the pack of cards in which only 3 king card present. Therefore, the probability of getting king in second draw is P(E2 ) = \(\frac{3}{51}\) = \(\frac{1}{17}\) . Now, since, both king cards which are drawing in first two draw is not replaced, therefore, total numbers of 50 cards are left in the pack of cards in which 4 ace cards are present. Therefore, the probability of getting ace in third draw is P(E3 ) = \(\frac{4}{50}\) = \(\frac{2}{25}\) . Since, all three events E1, E2 and E3 are independent. Therefore, the probability of getting first two cards as king and the third card as ace is P(E1 )P(E2 )P(E3 ) = \(\frac{1}{13} \times \frac{1}{17} \times \frac{2}{25}\) = \(\frac{2}{5525}\). Hence, the probability that first two cards are kings and the third card drawn is an ace is \(\frac{2}{5525}\). |
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