Question

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

Answer 1

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 face card is drawn There are 12 face cards in the pack of 52 cards
∴ 1 face card can be drawn in ¹²C₁ = 12 ways
∴ n(B) = 26

∴ P(B) = `("n"("B"))/("n"("S")) = 26/52`
There are 6 red face cards.
∴ n(A ∩ B) = 6
∴ P(A ∩ B) = `("n"("A" ∩ "B"))/("n"("S"))=6/52`
∴ Required probability = P(A ∪ B)
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)

= `26/52 + 12/52 - 6/52`

= `32/52`

= `8/13`