One card is drawn from a well-shuffled deck of 52 cards. Calculate the probability that the card will(i)         be an ace.(ii)        not be an ace.

Solution: Here, $n\left(S\right)=52$
(i) There are $4$ aces in a deck of 52 cards.
So, $E_A=4$
Probability card drawn is ace, $P\left(E_A\right)=\frac{E_A}{n\left(S\right)}=\frac{4}{52}=\frac{1}{13}$

(ii) There are $48$ cards that are not aces in a deck of 52 cards.
So, $E_{NA}=48$
Probability card drawn is not ace, $P\left(E_{NA}\right)=\frac{E_{NA}}{n\left(S\right)}=\frac{48}{52}=\frac{12}{13}$