A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is:
(i) not a diamond card
(ii) a black card

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 not a diamond card

Let E′ as the event that diamond card appears

$n (E^{′}) ={}^{13}C_1=13$

P (E′) = n (E′) / n (S)

= 13 / 52

= 1/4

So, P (E) = 1 – P (E′)

= 1 – 1/4

= 3/4

(ii) Let E be the event of drawing a black card

$n (E) ={}^{26}C_1 = 26$ (spades and clubs)

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

= 26 / 52

= 1/2