All the spades are taken out from a pack of c | vedclass

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(C) standard pack of cards contains $52$ cards. After removing all $13$ spades,we are left with $52 - 13 = 39$ cards.However,the question implies we a

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$\frac{1}{13}$

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(C) standard pack of cards contains $52$ cards. After removing all $13$ spades,we are left with $52 - 13 = 39$ cards.However,the question implies we are drawing from the $13$ spades only (as the ace of spades is one of them). Let the set of cards be the $13$ spades.The probability of not drawing the ace of spades in the $1^{st}$ draw is $\frac{12}{13}$.The probability of not drawing the ace of spades in the $2^{nd}$ draw,given it was not drawn in the $1^{st}$,is $\frac{11}{12}$.The probability of not drawing the ace of spades in the $3^{rd}$ draw,given it was not drawn in the first two,is $\frac{10}{11}$.The probability of drawing the ace of spades in the $4^{th}$ draw,given it was not drawn in the first three,is $\frac{1}{10}$.Thus,the required probability is $\frac{12}{13} 	imes \frac{11}{12} 	imes \frac{10}{11} 	imes \frac{1}{10} = \frac{1}{13}$.

All the spades are taken out from a pack of cards. From these cards,cards are drawn one by one without replacement until the ace of spades comes. The probability that the ace of spades comes in the $4^{th}$ draw is

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