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A card is drawn from a pack of 52 cards. What is the probability that, card is either red or black?

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#### Solution

One card can be drawn from the pack of 52 cards in ^{52}C_{1} = 52 ways

∴ n(S) = 52

Also, the pack of 52 cards consists of 26 red and 26 black cards.

Let A be the event that a red card is drawn

∴ Red card can be drawn in ^{26}C_{1} = 26 ways

∴ n(A) = 26

∴ P(A) = `("n"("A"))/("n"("S")) = 26/52`

Let B be the event that a black card is drawn

∴ Black card can be drawn in ^{26}C_{1} = 26 ways.

∴ n(B) = 26

∴ P(B) = `("n"("B"))/("n"("S")) = 26/52`

Since A and B are mutually exclusive and exhaustive events

∴ P(A ∩ B) = 0

∴ required probability = P(A ∪ B)

∴ P(A ∪ B) = P(A) + P(B) = `26/52+26/52` = 1

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