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

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Question

(A) The total number of cards is $52$. The number of spade cards is $13$.Probability of drawing a spade in one draw,$P(S) = \frac{13}{52} = \frac{1}{4

Vedclass · Accepted Answer

$\frac{9}{16}$

Vedclass · Answer

(A) The total number of cards is $52$. The number of spade cards is $13$.Probability of drawing a spade in one draw,$P(S) = \frac{13}{52} = \frac{1}{4}$.Probability of not drawing a spade in one draw,$P(S') = 1 - \frac{1}{4} = \frac{3}{4}$.Since the card is replaced each time,the events are independent.The probability that he fails the first two times means he does not get a spade in the first draw $AND$ he does not get a spade in the second draw.Required probability $= P(S') 	imes P(S') = \frac{3}{4} 	imes \frac{3}{4} = \frac{9}{16}$.

Outcome	Probability
$\omega_{1}$	$0.1$
$\omega_{2}$	$0.01$
$\omega_{3}$	$0.05$
$\omega_{4}$	$0.03$
$\omega_{5}$	$0.01$
$\omega_{6}$	$0.2$
$\omega_{7}$	$0.6$

$A$ 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 spade card. The probability that he will fail the first two times is:

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