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(C) Total number of cards $= 52$.Total number of face cards (jack,queen,king) $= 3 	imes 4 = 12$.Total number of non-face cards $= 52 - 12 = 40$.The

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$\frac{12}{85}$

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(C) Total number of cards $= 52$.Total number of face cards (jack,queen,king) $= 3 	imes 4 = 12$.Total number of non-face cards $= 52 - 12 = 40$.The event of getting a face card for the first time on the third turn means the first card is not a face card,the second card is not a face card,and the third card is a face card.Probability of no face card on the $1^{st}$ turn: $P(F_1^c) = \frac{40}{52}$.Probability of no face card on the $2^{nd}$ turn given no face card on the $1^{st}$ turn: $P(F_2^c | F_1^c) = \frac{39}{51}$.Probability of a face card on the $3^{rd}$ turn given no face cards on the $1^{st}$ and $2^{nd}$ turns: $P(F_3 | F_1^c \cap F_2^c) = \frac{12}{50}$.The required probability is $P = \frac{40}{52} 	imes \frac{39}{51} 	imes \frac{12}{50}$.Simplifying the expression:$P = \frac{10}{13} 	imes \frac{13}{17} 	imes \frac{6}{25} = \frac{10 	imes 13 	imes 6}{13 	imes 17 	imes 25} = \frac{10 	imes 6}{17 	imes 25} = \frac{60}{425} = \frac{12}{85}$.

Cards are drawn one-by-one without replacement from a well-shuffled pack of $52$ cards. The probability that a face card (jack,queen,or king) will appear for the first time on the third turn is equal to:

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