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

Answer:

Given : A standard deck of 52 cards.

To find : The probability of getting

(i) a king of red color

(ii) a face card

(iii) a red face card

(iv) the jack of hearts

(v) a spade

(vi) the queen of diamonds

Solution :

\text{Probability}=\frac{\text{Favorable outcome}}{\text{Total number of outcome}}Probability=

Total number of outcome

Favorable outcome

In a standard deck of 52 cards,

13 diamonds , 13 club , 13 hearts , 13 spade in which 12 face cards

(i) a king of red color

Favorable outcome = 2

Total number of outcome = 52

Probability of a king of red color drawn is

\text{Probability}=\frac{2}{52}=\frac{1}{26}Probability=

52

2

=

26

1

(ii) a face card

Favorable outcome = 12

Total number of outcome = 52

Probability of a face card drawn is

\text{Probability}=\frac{12}{52}=\frac{3}{13}Probability=

52

12

=

13

3

(iii) a red face card

Favorable outcome = 6

Total number of outcome = 52

Probability of a red face card drawn is

\text{Probability}=\frac{6}{52}=\frac{3}{26}Probability=

52

6

=

26

3

(iv) the jack of hearts

Favorable outcome = 1

Total number of outcome = 52

Probability of the jack of hearts drawn is

\text{Probability}=\frac{1}{52}Probability=

52

1

(v) a spade

Favorable outcome = 13

Total number of outcome = 52

Probability of a spade drawn is

\text{Probability}=\frac{13}{52}=\frac{1}{4}Probability=

52

13

=

4

1

(vi) the queen of diamonds

Favorable outcome = 1

Total number of outcome = 52

Probability of the queen of diamonds drawn is

\text{Probability}=\frac{1}{52}Probability=

52

1

Answer 2

Answer:

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

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