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(D) standard pack of playing cards contains $52$ cards,out of which $13$ are spades.The probability of drawing a spade in a single attempt is $P(S) =

Vedclass · Accepted Answer

$\frac{9}{16}$

Vedclass · Answer

(D) standard pack of playing cards contains $52$ cards,out of which $13$ are spades.The probability of drawing a spade in a single attempt is $P(S) = \frac{13}{52} = \frac{1}{4}$.The probability of not drawing a spade in a single attempt is $P(S') = 1 - \frac{1}{4} = \frac{3}{4}$.Since the card is replaced and the pack is shuffled after each draw,the events are independent.The probability of failing (not drawing a spade) in the first attempt is $\frac{3}{4}$.The probability of failing (not drawing a spade) in the second attempt is also $\frac{3}{4}$.Therefore,the probability of failing in both the first two attempts is $\frac{3}{4} 	imes \frac{3}{4} = \frac{9}{16}$.

$A$ person draws a card from a pack of playing cards,replaces it and shuffles the pack. He continues doing this until he draws a spade. The chance that he will fail in the first two attempts is

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