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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? - Mathematics and Statistics

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Sum

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 52C1 = 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 26C1 = 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 26C1 = 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

Concept: Addition Theorem of Probability
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