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

Sum

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

#### Solution

One card can be drawn from the pack of 52 cards in 52C1 = 52 ways.

∴ n(S) = 52

Let A ≡ the event that card drawn is a red card.
1 red card can be drawn from 26 red cards in 26C1 = 26 ways

∴ n(A) = 26

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

Let B ≡ the event that card drawn is a black card.
1 black card can be drawn from 26 black cards in 26C1 = 26 ways.

∴ n(B) = 26

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

Since A and B are mutually exclusive events,

P(A ∩ B) = 0

∴ required probability = P(A ∪ B)

= P(A) + P(B)

= 26/52 + 26/52

= 52/52

= 1

Alternative Method:

A pack of cards contains 26 black cards and 26 red cards.

When a card is drawn, it is either a black or red card. Therefore, the event is a sure event and hence the required probability is 1.

Concept: Addition Theorem for Two Events
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