A man draws a card from a pack of 52 playing | vedclass

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Question

(C) The total number of cards in a pack is $52$.The number of spade cards is $13$.The probability of drawing a spade card in a single trial is $P(S) =

Vedclass · Accepted Answer

$\frac{9}{64}$

Vedclass · Answer

(C) The total number of cards in a pack is $52$.The number of spade cards is $13$.The probability of drawing a spade card in a single trial is $P(S) = \frac{13}{52} = \frac{1}{4}$.The probability of not drawing a spade card (failure) in a single trial is $P(F) = 1 - P(S) = 1 - \frac{1}{4} = \frac{3}{4}$.Since the card is replaced and the pack is shuffled,each trial is independent.The probability that he fails the first two times is the probability of getting a non-spade card in the first trial $AND$ a non-spade card in the second trial.Required probability $= P(F) 	imes P(F) = \frac{3}{4} 	imes \frac{3}{4} = \frac{9}{64}$.

$A$ man draws a card from a pack of $52$ playing cards,replaces it,and shuffles the pack. He continues this process until he gets a card of spade. The probability that he will fail the first two times is

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