Question

A single card is drawn from a pack of 52 cards. What is the probability that the card is an ace or a king

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 an ace or a king

Let A be the event of getting an ace.

n(A) = 4C₁ = 4

Let B be the event of getting a king.

n(B) = 4C₁ = 4

P(getting an ace or a king)

= 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 + 4/52`

= `(4 + 4)/52`

= `8/52`

= `2/13`