One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

Question:

One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting

(i) a king of red colour

(ii) a face card

(iii) a red face card

(iv) the jack of hearts

(vi) the queen of diamonds

Solution:

Total number of cards in a well-shuffled deck = 52

(i) Total number of kings of red colour = 2

$P$ (getting a king of red colour) $=\frac{\text { Number of favourable outcomes }}{\text { Number of total possible outcomes }}$

$=\frac{2}{52}=\frac{1}{26}$

$=\frac{2}{52}=\frac{1}{26}$

$P($ getting a face card $)=\frac{\text { Number of favourable outcomes }}{\text { Number of total possible outcomes }}$

$=\frac{12}{52}=\frac{3}{13}$

(iii) Total number of red face cards = 6

$P($ getting a red face card $)=\frac{\text { Number of favourable outcomes }}{\text { Number of total possible outcomes }}$

$=\frac{6}{52}=\frac{3}{26}$

(iv) Total number of Jack of hearts = 1

$P$ (getting a Jack of hearts) $=\frac{\text { Number of favourable outcomes }}{\text { Number of total possible outcomes }}$

$=\frac{1}{52}$

(v) Total number of spade cards = 13

$P($ getting a spade card $)=\frac{\text { Number of favourable outcomes }}{\text { Number of total possible outcomes }}$

$=\frac{13}{52}=\frac{1}{4}$

(vi) Total number of queen of diamonds = 1

$P$ (getting a queen of diamond) $=\frac{\text { Number of favourable outcomes }}{\text { Number of total possible outcomes }}$

$=\frac{1}{52}$