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

Answer:

total no. of cards =52

i no. of red kings- 2

P ( of getting a king of red colour)

= 2/52

=1/26

ii no. of face cards=12

P ( of getting a face card )

=12/52

=3/13

iii no. of red face cards= 3+3=6

P (of getting a red face card)=6/52

= 3/26

iv no. of Jack(of hearts)= 1

P (of getting a Jack of hearts)= 1/52

v. no. of spades = 13

P ( of getting a spade) = 13/52=1/4

vi a queen of diamond =1

P (of getting a queen of diamond)= 1/52

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