A card is drawn at random from a pack of well-shuffled 52 playing cards. Find the probability that the card drawn is (1) an ace (2) a spade.

Answer

(1) `(1)/(13)`
(2) `(1)/(4)`

Explanation

S is the sample space
`thereforen(S)=52" "....("There are 52 playing cards")`
(1) Let A be the event that the card drawn is an ace. There are four suits,Spade,Heart,Diamond and Club. Each suit has one ace.
`thereforen(A)={4}`
`P(A)=(n(A))/(n(S))=(4)/(52)=(1)/(13).`
(2) Let B be the event that the card drawn is a spade.
There are 13 cards in the suit of spade
One spade can be drawn out of 13 spade cards in 13 ways.
`thereforen(B)=13`
`P(B)=(n(B))/(n(S))=(13)/(52)=(1)/(4)`