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

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)

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

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