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

Answer: 

Possible numbers of events = 52

(i) Numbers of king of red colour = 2
Probability of getting a king of red colour = 2/52 = 1/26

(ii) Numbers of face cards = 12
Probability of getting a face card = 12/52 = 3/13

(iii) Numbers of red face cards = 6
Probability of getting a king of red colour = 6/52 = 3/26

(iv) Numbers of jack of hearts =1
Probability of getting a king of red colour = 1/526

(v) Numbers of king of spade = 13
Probability of getting a king of red colour = 13/52 = 1/4

(vi) Numbers of queen of diamonds = 1
Probability of getting a king of red colour = 1/52

Total number of outcomes = 52

(i) Let E₁ be the event of getting a king of red suit.

Number of favorable outcomes  = 2

Therefore, P(getting of red suit) = P(E₁) = \(\frac{number\,of\,outcomes\,favorable\,to\,E_1}{number\,of\,all\,possible\,outcomes}\) = \(\frac{2}{52}\) = \(\frac{1}{36}\).

Thus, the probability of getting a king of red suit is \(\frac{1}{36}\).

(ii) Let E₂ be the event of getting a face card

Number of favorable outcomes = 12

Therefore, P(getting of red suit) = P(E₂) = \(\frac{number\,of\,outcomes\,favorable\,to\,E_2}{number\,of\,all\,possible\,outcomes}\) = \(\frac{12}{52}\) = \(\frac{3}{13}\)

Thus, the probability of getting a face card is \(\frac{3}{13}\).

(iii) Let E₃ be the event of getting red face card

Number of favorable outcomes = 6

Therefore, P(getting of red suit) = P(E₃) = \(\frac{number\,of\,outcomes\,favorable\,to\,E_3}{number\,of\,all\,possible\,outcomes}\) = \(\frac{6}{52}\) = \(\frac{3}{26}\)

Thus, the probability of getting a red face card is \(\frac{3}{26}\).

Total number of outcomes = 52

(i) Let E₄ be the event of getting a queen of black suit.

Number of favorable outcomes = 2

Therefore, P(getting a queen of black suit) = P(E₄) = \(\frac{number\,of\,outcomes\,favorable\,to\,E_4}{number\,of\,all\,possible\,outcomes}\) = \(\frac{2}{52}\) = \(\frac{1}{26}\)

Thus, the probability of getting a queen of black suit is \(\frac{1}{26}\).

(ii) let E₅ be the event of getting a jack of hearts.

Number of favorable outcomes = 1

 Therefore, P(getting a queen of black suit) = P(E₅) = \(\frac{number\,of\,outcomes\,favorable\,to\,E_5}{number\,of\,all\,possible\,outcomes}\) = \(\frac{1}{52}\)

Thus, the probability of getting a jack of heart is \(\frac{1}{52}\).

(iii) let E₆ be the event of getting a spade.

 Number of favorable outcomes = 13

 Therefore, P(getting a queen of black suit) = P(E₆) = \(\frac{number\,of\,outcomes\,favorable\,to\,E_6}{number\,of\,all\,possible\,outcomes}\) = \(\frac{13}{52}\) = \(\frac{1}{4}\)

Thus, the probability of getting a spade is \(\frac{1}{4}\).