Question

A single card is drawn from a pack of 52 cards. What is the probability that the card will be 6 or smaller

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 will be 6 or smaller:

Let A be the event of getting a number 6.

∴ n(A) = 4C₁ = 4

Let B be the event of getting numbers less than 6.

n(B) = 16C₁ = 16

P (the card will be 6 or less than 6)

= P(A or B)

= P(A ∪ B)

= P(A) + P(B)

(since A and B are mutually exclusive events A ∩ B = Φ)

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

= `4/52 + 16/52`

= `(4 + 16)/52`

= `20/52`

= `5/13`