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Question

(A) Let $K$ denote the event that the card drawn is a king and $A$ be the event that the card drawn is an ace. We need to find the probability $P(KKA)

Vedclass · Accepted Answer

$\frac{2}{5525}$

Vedclass · Answer

(A) Let $K$ denote the event that the card drawn is a king and $A$ be the event that the card drawn is an ace. We need to find the probability $P(KKA)$.The probability of drawing the first king is $P(K_1) = \frac{4}{52}$.After drawing one king,there are $51$ cards remaining,including $3$ kings. The probability of drawing the second king is $P(K_2|K_1) = \frac{3}{51}$.After drawing two kings,there are $50$ cards remaining,including $4$ aces. The probability of drawing an ace is $P(A_3|K_1 \cap K_2) = \frac{4}{50}$.By the multiplication rule of probability:$P(KKA) = P(K_1) 	imes P(K_2|K_1) 	imes P(A_3|K_1 \cap K_2)$$P(KKA) = \frac{4}{52} 	imes \frac{3}{51} 	imes \frac{4}{50}$$P(KKA) = \frac{1}{13} 	imes \frac{1}{17} 	imes \frac{2}{25} = \frac{2}{5525}$.

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

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