**Question:**

A card is selected from a pack of 52 cards.

(a) How many points are there in the sample space?

(b) Calculate the probability that the card is an ace of spades.

(c) Calculate the probability that the card is

(i) an ace

(ii) black card.

**Solution:**

(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, $n(F)=26$

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

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