Question

One card is randomly drawn from a deck of 52 playing cards. Find the probability that
(i) the drawn card is red.
(ii) the drawn card is an ace.
(iii) the drawn card is red and a king.
(iv) the drawn card is red or a king.

Answer 1

In randomly drawing a card from 52 cards, the possible outcome is 52. i.e., n(S) = 52
(i) Let A denotes the event that the drawn card is red. Since the number of red cards is 26. So, n(A) = 26
$\therefore$ P(A = a red card) $=\frac{n\left(A\right)}{n\left(S\right)}=\frac{26}{52}=\frac{1}{2}$

ii) Let B denotes the event that the drawn card is an ace. Since there are four aces in the deck
So, n(B) = 4
$\therefore$ P(B = an ace card) $=\frac{n\left(B\right)}{n\left(S\right)}=\frac{4}{52}=\frac{1}{13}$

iii) Let C denotes the event that the drawn card is red and a king. Since there are only two cards which are red kings.
So, n(C) = 2
$\therefore$ P(C = card is red and a king)
$=\frac{n\left(C\right)}{n\left(S\right)}=\frac{2}{52}=\frac{1}{26}$

iv) Let D denotes the event that the drawn card is red or a king. We have 26 red cards, which include 2 kings and there are two more kings of black colour.
So, n(D) = 26 + 2 = 28
$\therefore$ P(D = card is red or a king)
$=\frac{n\left(D\right)}{n\left(S\right)}=\frac{28}{52}=\frac{7}{13}$