Question

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

Answer 1

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 black card. 1 black card can be drawn from 26 black 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 face card. 1 face card can be dra\vn from 12 face cards in ¹²C₁ = 12 ways

∴ n(B) = 12

∴ P(B) = `("n"("B"))/("n"("S")) = 12/52`

Since 6 cards are common between A and B,

n(A ∩ B) = 6

∴ P(A ∩ B) = `("n"("A" ∩ "B"))/("n"("S")) = 6/52` 

∴ required probability = P (A U B)

= P(A) + P(B) - P(A ∩ B)

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

`= 32/52` i.e., `=8/13`