A person draws a card from a pack of 52 cards | vedclass

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Question

(A) Let $E$ be the event of drawing a red card. The probability of drawing a red card in a single draw is $P(E) = \frac{13}{52} = \frac{1}{4}$.The pro

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$\frac{9}{64}$

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(A) Let $E$ be the event of drawing a red card. The probability of drawing a red card in a single draw is $P(E) = \frac{13}{52} = \frac{1}{4}$.The probability of not drawing a red card is $P(\overline{E}) = 1 - \frac{1}{4} = \frac{3}{4}$.We want the probability that the first red card appears on the third draw. This means the first two draws must be non-red cards and the third draw must be a red card.The required probability is $P(\overline{E} \cap \overline{E} \cap E) = P(\overline{E}) 	imes P(\overline{E}) 	imes P(E)$.Substituting the values: $P = \frac{3}{4} 	imes \frac{3}{4} 	imes \frac{1}{4} = \frac{9}{64}$.

$x = x_{i}$	$0$	$1$	$2$
$P_{i}$	$\frac{25}{36}$	$\frac{5}{18}$	$\frac{1}{36}$

$A$ person draws a card from a pack of $52$ cards and replaces it. After shuffling,he draws a card again. If he repeats this process,what is the probability that he draws a red card for the first time on the third draw?

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