Question

A card is selected at random from well-shuffled pack of $52$ cards. Find the probability that the selected card is
(1) a black coloured queen.
(2) not a king.

Answer 1

For the given experiment, the number of equally likely outcomes is $52$
$n=52$
(i) Let $A$ be the event that the selected card is a black coloured queen.
The number of favourable outcomes is $2$ (i.e., queen of spade or club)
$P\left(A\right)=\frac{2}{52}=\frac{1}{26}$
(ii) Let $B$ be the event that the selected card is a king. The number of favourable outcomes is $4$ as there contains $4$ kings in a pack of $52$ cards.
$P\left(B\right)=\frac{4}{52}=\frac{1}{13}$
Then $B^{\prime }$ is the event that the selected card is not king.
Then, $P\left(B^{\prime }\right)=1-P\left(B\right)=1-\frac{1}{13}=\frac{12}{13}$

Hence, the answer is $\frac{12}{13}$.