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(C) The total number of cards is $52$. Since the cards are drawn with replacement, the events $A$ and $B$ are independent. Event $A$ is drawing a face

Vedclass · Accepted Answer

$\frac{3}{4}$

Vedclass · Answer

(C) The total number of cards is $52$. Since the cards are drawn with replacement, the events $A$ and $B$ are independent. Event $A$ is drawing a face card in the first draw. There are $12$ face cards in a deck ($4$ Jacks, $4$ Queens, $4$ Kings). Thus, $P(A) = \frac{12}{52} = \frac{3}{13}$. Event $B$ is drawing a club card in the second draw. There are $13$ club cards in a deck. Thus, $P(B) = \frac{13}{52} = \frac{1}{4}$. Since the events are independent, $P(B|A) = P(B) = \frac{1}{4}$. We need to find $P(\overline{B}|A)$. Using the property of complementary events, $P(\overline{B}|A) = 1 - P(B|A)$. $P(\overline{B}|A) = 1 - \frac{1}{4} = \frac{3}{4}$. Therefore, the correct option is $C$.

Two cards are drawn randomly from a pack of $52$ playing cards one after the other with replacement. If $A$ is the event of drawing a face card in the first draw and $B$ is the event of drawing a club card in the second draw, then $P(\overline{B}|A) = $

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