Question

A card is drawn from a well shuffled deck of $52$ cards. Find the probability of getting (i) a king of red colour (ii) a face card (iii) the queen of diamonds.

Answer 1

Total number of cards in a deck of cards $=52$
Total number of outcomes $=52$
(i) Let $A$ denote the event of getting a king of red colour.
There are two cards in favour of getting a king of red colour i.e., King of heart and King of diamond.
Number of outcomes in favour of event $A=2$
$\therefore P\left(A\right)=\frac{2}{52}=\frac{1}{26}$
(ii) Let $B$ denote the event of getting a face card.
There are $12$ cards in favour of getting a face card i.e., $4$ King, $4$ Queen and $4$ Jack cards.
Number of outcomes in favour of event $B=12$
$\therefore P\left(B\right)=\frac{12}{52}=\frac{3}{13}$
(iii) Let $C$ denote the event of getting a queen of diamond.
There is one queen of diamond in the deck of cards.
Number of outcomes in favour of event $C=1$
$\therefore P\left(C\right)=\frac{1}{52}$