A deck consists of 4 Aces,4 Kings,4 Queens,an | vedclass

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Question

(A) Total number of cards = $16$. Number of ways to draw $2$ cards from $16$ is $\binom{16}{2} = \frac{16 	imes 15}{2} = 120$. Number of Aces = $4$.

Vedclass · Accepted Answer

$\frac{9}{20}$

Vedclass · Answer

(A) Total number of cards = $16$. Number of ways to draw $2$ cards from $16$ is $\binom{16}{2} = \frac{16 	imes 15}{2} = 120$. Number of Aces = $4$. Number of non-Ace cards = $12$. The probability of getting no Ace is the probability of drawing $2$ cards from the $12$ non-Ace cards. $P(	ext{no Ace}) = \frac{\binom{12}{2}}{\binom{16}{2}} = \frac{\frac{12 	imes 11}{2}}{120} = \frac{66}{120} = \frac{11}{20}$. The probability of getting at least one Ace is $1 - P(	ext{no Ace})$. $P(	ext{at least one Ace}) = 1 - \frac{11}{20} = \frac{9}{20}$.

$A$ deck consists of $4$ Aces,$4$ Kings,$4$ Queens,and $4$ Jacks. If $2$ cards are drawn at random from this deck of $16$ cards,what is the probability that at least one card is an Ace?

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