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

(v) a spade

(vi) the queen of diamonds​

Answer 1

Given :-

One card is drawn from a well-shuffled deck of 52 cards

Total number of possible outcomes = 52

To 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

(v) a spade

(vi) the queen of diamonds

Formulae :-

$P(E) = \frac{Number \: of \: favourable \: outcomes}{Total \: number \: of \: outcomes}$

Solution :-

(i) Total numbers of king of red colour = 2

$P (getting \: a \: king \: of \: red \: colour) = \frac{2}{52} = > \frac{1}{26}$

(ii) Total numbers of face cards = 12

$P (getting a face card) = \frac{12}{52} = \frac{3}{13}$

(iii) Total numbers of red face cards = 6

$P (getting \: a \: king \: of \: red \: colour) = \frac{6}{52} = \frac{3}{26}$

(iv) Total numbers of jack of hearts = 1

$P (getting \: a \: king \: of \: red \: colour) = \frac{1}{52}$

(v) Total numbers of king of spade = 13

$P (getting \: a \: king \: of \: red \: colour) = \frac{13}{52} = \frac{1}{4}$

(vi) Total numbers of queen of diamonds = 1

$P (getting \: a \: king \: of \: red \: colour) = \frac{1}{52}$

Answer 2

SOLUTION :-

(i) Total numbers of king of red colour = 2

$P (getting \: a \: king \: of \: red \: colour) = \frac{2}{52} = > \frac{1}{26}$

(ii) Total numbers of face cards = 12

$P (getting a face card) = \frac{12}{52} = \frac{3}{13}$

(iii) Total numbers of red face cards = 6

$P (getting \: a \: king \: of \: red \: colour) = \frac{6}{52} = \frac{3}{26}$

(iv) Total numbers of jack of hearts = 1

$P (getting \: a \: king \: of \: red \: colour) = \frac{1}{52}$

(v) Total numbers of king of spade = 13

$P (getting \: a \: king \: of \: red \: colour) = \frac{13}{52} = \frac{1}{4}$

(vi) Total numbers of queen of diamonds = 1

$P (getting \: a \: king \: of \: red \: colour) = \frac{1}{52}$