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

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Question

(C) standard pack of $52$ cards contains $12$ face cards (Jack,Queen,King of each suit). There are $6$ black face cards (Jack,Queen,King of Spades and

Vedclass · Accepted Answer

$\frac{11}{312}$

Vedclass · Answer

(C) standard pack of $52$ cards contains $12$ face cards (Jack,Queen,King of each suit). There are $6$ black face cards (Jack,Queen,King of Spades and Clubs). The first card drawn is a queen. There are $4$ queens in total. Case $1$: If the first card is a black queen (Spades or Clubs),there are $5$ black face cards remaining out of $51$ cards. Case $2$: If the first card is a red queen (Hearts or Diamonds),there are $6$ black face cards remaining out of $51$ cards. However,the question asks for the probability given the first card is a queen. Total queens = $4$. Black queens = $2$,Red queens = $2$. Probability of drawing a black face card = $P(	ext{Black Face Card} | 	ext{Black Queen}) 	imes P(	ext{Black Queen}) + P(	ext{Black Face Card} | 	ext{Red Queen}) 	imes P(	ext{Red Queen})$ $= (\frac{5}{51} 	imes \frac{2}{4}) + (\frac{6}{51} 	imes \frac{2}{4}) = \frac{10}{204} + \frac{12}{204} = \frac{22}{204} = \frac{11}{102}$. Wait,re-evaluating: The question implies the first card is a queen. There are $4$ possible queens. If the first card is a black queen (probability $1/2$ given it is a queen),$5$ black face cards remain. If the first card is a red queen (probability $1/2$ given it is a queen),$6$ black face cards remain. Probability $= (\frac{1}{2} 	imes \frac{5}{51}) + (\frac{1}{2} 	imes \frac{6}{51}) = \frac{11}{102}$. Given the options provided,let us re-check the calculation. If the question implies the first card is a specific queen,the answer is $11/102$. None of the options match. Assuming the question meant 'a black queen' or similar,but based on standard interpretation,the result is $11/102$.

Two cards are drawn from a pack of $52$ playing cards one after the other without replacement. If the first card drawn is a queen,then the probability of getting a face card from a black suit in the second draw is

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