Question

One card is drawn from a pack of $52$ cards, each of the $52$ cards being equally likely to be drawn. Find the probability that the cards drawn is
i. an ace
ii. either red or king
iii. a face card.

Answer 1

Total cards $n\left(S\right)=52$

(i) There are four ace cards in pack

$n\left(A\right)=4$

$p\left(A\right)=\frac{n\left(A\right)}{n\left(S\right)}=\frac{4}{52}=\frac{1}{13}$

(ii) There are $26$ red cards in a pack and two black king

$n\left(B\right)=26+2=28$

$P\left(B\right)=\frac{n\left(B\right)}{n\left(S\right)}=\frac{28}{52}=\frac{7}{13}$

(iii) In a pack of $52$ cards : kings queen jacks are called face cards.

$P\left(C\right)=\frac{n\left(C\right)}{n\left(S\right)}=\frac{12}{52}=\frac{3}{13}$