Question

A single card is drawn from a pack of 52 cards. What is the probability that the card is either a queen or 9?

Answer 1

S be the sample space one card is drawn from a pack of 52 cards.

∴ n(S) = 52C₁

n(S) = 52

The card is either a queen or 9?

Let A be the event of getting a Queen.

∴ n(A) = 4C₁ = 4

Let B be the event of getting a number 9.

n(B) = 4C₁ = 4

P (the card is either a Queen or 9)

= P(A or B)

= P(A ∪ B

= P(A) + P(B)

(since A and B are mutually exclusive events)

= `("n"("A"))/("n"("S")) + ("n"("B"))/("n"("S"))`

= `4/52 + 4/52`

= `(4 + 4)/52`

= `8/52`

= `2/13`