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.

Answer 1

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)
∴ ${\mathrm{P}}_{\left(4\mathrm{card}\right)}=\frac{4}{52}=\frac{1}{13}$
(ii) There are 4 queens in a pack of cards (queen of hearts, queen of diamonds, queen of spades and queen of cloves)
∴ ${\mathrm{P}}_{\left(\mathrm{queen}\right)}=\frac{4}{52}=\frac{1}{13}$
(iii) There are a total of 26 black cards (13 spade cards and 13 clove cards)
∴ ${\mathrm{P}}_{\left(\mathrm{black}\mathrm{card}\right)}=\frac{26}{52}=\frac{1}{2}$