From a well-shuffled pack of 52 playing cards | vedclass

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(C) Since the cards are drawn with replacement,each draw is an independent event.Let $E$ be the event of drawing a "king of hearts". The probability o

Vedclass · Accepted Answer

$\frac{51^4}{52^5}$

Vedclass · Answer

(C) Since the cards are drawn with replacement,each draw is an independent event.Let $E$ be the event of drawing a "king of hearts". The probability of drawing a "king of hearts" in any single draw is $P(E) = \frac{1}{52}$.The probability of not drawing a "king of hearts" in any single draw is $P(E') = 1 - \frac{1}{52} = \frac{51}{52}$.We want the $5^{th}$ card to be a "king of hearts". The first $4$ cards can be any card other than the "king of hearts",and the $5^{th}$ card must be the "king of hearts".Probability = $P(E') 	imes P(E') 	imes P(E') 	imes P(E') 	imes P(E) = \left(\frac{51}{52}ight)^4 	imes \frac{1}{52} = \frac{51^4}{52^5}$.

$X=x$	$0$	$1$	$2$	$3$
$P(X=x)$	$\frac{1}{3}$	$\frac{1}{2}$	$0$	$\frac{1}{6}$

From a well-shuffled pack of $52$ playing cards,cards are drawn one by one with replacement. The probability that the $5^{th}$ card will be the "king of hearts" is:

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