Question 77

From a well shuffled pack of 52 cards, 3 cards are drawn successively, the first being replaced before the second is drawn and the second being replaced before the third is drawn. The probability that the first is black, the second is diamond and the third is ace. 

Since, three cards are drawn successively after replacing the previous one. 

Probability of drawing first card which is Black = $$\frac{26C1}{52C1} = \frac{26}{52} = \frac{1}{2}$$

Probability of drawing second card which is Diamond = $$\frac{13C1}{52C1} = \frac{13}{52} = \frac{1}{4}$$

Probability of drawing third card which is Ace= $$\frac{4C1}{52C1} = \frac{4}{52} = \frac{1}{13}$$

Required probability = $$\frac{1}{2} * \frac{1}{4} * \frac{1}{13} = \frac{1}{104}$$

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