A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is:
(i) neither an ace nor a king
(ii) spade or an ace

A Pack of 52 cards is given

By using the formula of probability, we get,

P (E) = favourable outcomes / total possible outcomes

We know, a card is drawn from a pack of 52 cards, so number of elementary events in the sample space will be,

$n(S)={}^{52}C_1=52$

(i) Let E be the event of drawing neither a heart nor a king

Let E′ as the event that either a heart or king appears

$n(E^{‘})={}^6C_1+{}^4C_1-1=16$ (there is a heart king so it is deducted)

P (E′) = n (E′) / n (S)

= 16 / 52

= 4/13

So, P (E) = 1 – P (E′)

= 1 – 4/13

= 9/13

(ii) Let E be the event of drawing a spade or king

$n(E)={}^13C_1+{}^4C_1-1=16$

P (E) = n (E) / n (S)

= 16 / 52

= 4/13