A card is selected from a pack of 52 cards.

(a) When a card is selected from a pack of 52 cards, the number of possible outcomes is 52 i.e., the sample space contains 52 elements.

Therefore, there are 52 points in the sample space.

(b) Let A be the event in which the card drawn is an ace of spades.

Accordingly, $n(\mathrm{~A})=1$

$\therefore \mathrm{P}(\mathrm{A})=\frac{\text { Number of outcomes favourable to } \mathrm{A}}{\text { Total number of possible outcomes }}=\frac{n(\mathrm{~A})}{n(\mathrm{~S})}=\frac{1}{52}$

(c) (i)Let E be the event in which the card drawn is an ace.

Since there are 4 aces in a pack of 52 cards, $n(E)=4$

$\therefore P(E)=\frac{\text { Number of outcomes favourable to } E}{\text { Total number of possible outcomes }}=\frac{n(E)}{n(S)}=\frac{4}{52}=\frac{1}{13}$

(ii)Let F be the event in which the card drawn is black.

Since there are 26 black cards in a pack of 52 cards, $n(F)=26$

$\therefore \mathrm{P}(\mathrm{F})=\frac{\text { Number of outcomes favourable to } \mathrm{F}}{\text { Total number of possible outcomes }}=\frac{n(\mathrm{~F})}{n(\mathrm{~S})}=\frac{26}{52}=\frac{1}{2}$