**Question:**

One card is drawn at random from a well-shuffled deck of 52 cards. Find the probability that the card drawn is

(i) a king

(ii) a spade

(iii) a red queen

(iv) a black 8.

**Solution:**

Total number of possible outcomes $=52$

(i) There are 4 kings cards (king of hearts, king of diamonds, king of spades and king of cloves)

Number of kings $=4$

$\therefore \mathrm{P}_{(\text {king })}=\frac{4}{52}=\frac{1}{13}$

(ii) There is a total of 13 spades cards.

Number of spades $=13$

$\therefore \mathrm{P}_{(\text {spades })}=\frac{13}{52}=\frac{1}{4}$

(iii) There are 2 red queens in a pack (queen of hearts and queen of diamonds)

Number of red queens $=2$

$\therefore \mathrm{P}_{(\text {red }) \text { queen })}=\frac{2}{52}=\frac{1}{26}$

(iv) There are 2 black $8 \mathrm{~s}$ in a pack (8 of cloves and 8 of spades)

Number of black $8 \mathrm{~s}=2$

$\therefore \mathrm{P}_{(\text {black } 8)}=\frac{2}{52}=\frac{1}{26}$