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
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Answer 1

$<font color="green">$★FIND:

➡️(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

$<font color="red">$★GIVEN,

Total number of possible outcomes = 52

One card is drawn from a well-shuffled deck of 52 cards=1/52

$<font color="blue">$★SOLUTION:

WE KNOW THAT:

P(E) = (Number of favourable outcomes/ Total number of outcomes)

$<font color="orange">$➡️(i)Total numbers of king of red colour = 2

P(getting a king of red colour) = 2/52

➡️1/26➡️0.038

$<font color="purple">$➡️(ii) Total numbers of face cards = 12

P(getting a face card) = 12/52

➡️3/13 ➡️0.23

$<font color="violet">$➡️(iii)Total numbers of red face cards = 6

P(getting a king of red colour) = 6/52

➡️3/26➡️0.11

$<font color="green">$➡️(iv)Total numbers of jack of hearts = 1

P(getting a king of red colour) = 1/52

➡️0.019

$<font color="red">$➡️(v)Total numbers of king of spade = 13

P(getting a king of red colour) = 13/52

➡️1/4➡️0.25

$<font color="purple">$➡️(vi)Total numbers of queen of diamonds = 1

P(getting a king of red colour) = 1/52

➡️ 0.019

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

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