A draws two cards with replacement from a pac | vedclass

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Question

(C) The probability of $A$ drawing two cards of the same suit with replacement:There are $4$ suits,each with $13$ cards.The probability of picking a c

Vedclass · Accepted Answer

$\frac{5}{144}$

Vedclass · Answer

(C) The probability of $A$ drawing two cards of the same suit with replacement:There are $4$ suits,each with $13$ cards.The probability of picking a card of a specific suit is $\frac{13}{52} = \frac{1}{4}$.Since the cards are drawn with replacement,the probability of drawing two cards of the same suit is $4 	imes (\frac{1}{4} 	imes \frac{1}{4}) = 4 	imes \frac{1}{16} = \frac{1}{4}$.The probability of $B$ throwing a total of $6$ with a pair of dice:The total outcomes when throwing two dice is $6 	imes 6 = 36$.The favorable outcomes for a sum of $6$ are $(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)$,which are $5$ outcomes.So,$P(B) = \frac{5}{36}$.Since $A$ and $B$ are independent events,the combined probability is:$P(A \cap B) = P(A) 	imes P(B) = \frac{1}{4} 	imes \frac{5}{36} = \frac{5}{144}$.

$A$ draws two cards with replacement from a pack of $52$ cards and $B$ throws a pair of dice. What is the chance that $A$ gets both cards of the same suit and $B$ gets a total of $6$?

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