Question

A card is drawn at random from a well-shuffled pack of $52$ playing cards. Find the probability of the events that the card drawn is:
$\left(a\right)$ a king $\left(b\right)$ a face card

Answer 1

Let $S$ be the sample space.
There are $52$ playing cards in a pack
$\therefore$ $n\left(S\right)=52$
Let $A$ be the event that the card drawn is a king
Total king in pack $=4$
$\therefore$ $n\left(A\right)=4$
$\therefore$ $P\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{4}{52}=\frac{1}{13}$
Let $B$ be the event that the card drawn is a face card
Total face card in a pack $=12$
$\therefore$ $n\left(B\right)=12$
$\therefore$ $P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}=\frac{12}{52}=\frac{3}{13}$