Question

From a pack of 52 playing card, Jacks, Queens and Kings of red colour are removed. From the remaining, a card is drawn at random. Find the probability that drawn card is:

(i) a black King, (ii) a card of red colour, (iii) a card of black colour.

Answer 1

Since, Jacks, Queens and Kings of red colour are removed. Then,

Total number of possible outcomes = $52-6=46$

(i) Let $E_1$ be the event of getting a black king

$\therefore$ Favourable outcomes = King of spade and King of club.

No. of favourable outcomes = 2

$P\left(E_1\right)=\frac{2}{46}=\frac{1}{23}$

(ii) Let$E_2$ be the event of getting a card of red colour

$\therefore$ Favourable outcomes = 10 cards of heart and

10 cards of diamond.

No. of favourable outcomes = 20

$P\left(E_2\right)=\frac{20}{46}=\frac{10}{23}$

(iii) Let $E_3$ be the event of getting a card of black colour

$\therefore$ Favourable outcomes = 13 cards of spade and 13 cards of club.

No. of favourable outcomes = 26

$P\left(E_3\right)=\frac{20}{46}=\frac{10}{23}$