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 4
(ii) a queen
(iii) a black card.
Solution:
Total number of possible outcomes $=52$
(i) There are 4 cards of with the number 4 (4 of hearts, 4 of diamonds, 4 of spades and 4 of cloves)
$\therefore \mathrm{P}_{(4 \text { card })}=\frac{4}{52}=\frac{1}{13}$
(ii) There are 4 queens in a pack of cards (queen of hearts, queen of diamonds, queen of spades and queen of cloves) $\therefore \mathrm{P}_{(\text {queen })}=\frac{4}{52}=\frac{1}{13}$
(iii) There are a total of 26 black cards (13 spade cards and 13 clove cards)
$\therefore \mathrm{P}_{\text {(black card) }}=\frac{26}{52}=\frac{1}{2}$