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.

Answer 1

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$=4$
∴ ${\mathrm{P}}_{\left(\mathrm{king}\right)}=\frac{4}{52}=\frac{1}{13}$

(ii) There is a total of 13 spades cards.
Number of spades$=13$
∴ ${\mathrm{P}}_{\left(\mathrm{spades}\right)}=\frac{13}{52}=\frac{1}{4}$
(iii) There are 2 red queens in a pack (queen of hearts and queen of diamonds)
Number of red queens $=2$
∴ ${\mathrm{P}}_{\left(\mathrm{red}\mathrm{queen}\right)}=\frac{2}{52}=\frac{1}{26}$

(iv) There are 2 black 8s in a pack (8 of cloves and 8 of spades)
Number of black 8s $=2$
∴ ${\mathrm{P}}_{\left(\mathrm{black}8\right)}=\frac{2}{52}=\frac{1}{26}$