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