Two cards are drawn from a pack of 52 cards. | vedclass

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(C) The total number of ways to draw $2$ cards from $52$ cards is $^{52}C_2$.Let $A$ be the event that both cards are red.Let $B$ be the event that bo

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$55/221$

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(C) The total number of ways to draw $2$ cards from $52$ cards is $^{52}C_2$.Let $A$ be the event that both cards are red.Let $B$ be the event that both cards are kings.We need to find $P(A \cup B) = P(A) + P(B) - P(A \cap B)$.There are $26$ red cards,so the number of ways to choose $2$ red cards is $^{26}C_2$.$P(A) = \frac{^{26}C_2}{^{52}C_2} = \frac{325}{1326}$.There are $4$ kings,so the number of ways to choose $2$ kings is $^4C_2$.$P(B) = \frac{^4C_2}{^{52}C_2} = \frac{6}{1326} = \frac{1}{221}$.$A \cap B$ is the event that both cards are red kings. There are $2$ red kings (King of Hearts and King of Diamonds),so the number of ways to choose $2$ red kings is $^2C_2 = 1$.$P(A \cap B) = \frac{^2C_2}{^{52}C_2} = \frac{1}{1326}$.Using the formula: $P(A \cup B) = \frac{325}{1326} + \frac{6}{1326} - \frac{1}{1326} = \frac{330}{1326}$.Simplifying the fraction: $\frac{330}{1326} = \frac{55}{221}$.

Two cards are drawn from a pack of $52$ cards. What is the probability that both cards are red or both cards are kings?

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