Two cards are drawn from a pack of 52 cards. | vedclass

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(A) Total number of ways to draw $2$ cards from $52$ is $^{52}C_2 = \frac{52 	imes 51}{2} = 1326$. Number of ways to draw $2$ cards such that none of

Vedclass · Accepted Answer

$\frac{33}{221}$

Vedclass · Answer

(A) Total number of ways to draw $2$ cards from $52$ is $^{52}C_2 = \frac{52 	imes 51}{2} = 1326$. Number of ways to draw $2$ cards such that none of them is an ace (i.e.,choosing from $48$ non-ace cards) is $^{48}C_2 = \frac{48 	imes 47}{2} = 1128$. Probability of drawing no ace is $P(	ext{no ace}) = \frac{1128}{1326} = \frac{47 	imes 24}{51 	imes 13} = \frac{47 	imes 8}{17 	imes 13} = \frac{376}{663} = \frac{48}{52} 	imes \frac{47}{51} = \frac{12}{13} 	imes \frac{47}{51} = \frac{4}{13} 	imes \frac{47}{17} = \frac{188}{221}$. Therefore,the probability that at least one card is an ace is $1 - P(	ext{no ace}) = 1 - \frac{188}{221} = \frac{221 - 188}{221} = \frac{33}{221}$.

Two cards are drawn from a pack of $52$ cards. What is the probability that at least one of the cards drawn is an ace?

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