One card is drawn from well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red suit, (ii) a face card, (iii) a red face card, (iv) a queen of black suit, (v) a jack of hearts, (vi) a spade.
Total numbers of elementary events are: 52
(i) Let E be the event of getting a king of red suit
Then, the favourable numbers of outcomes are: 2
∴ P (king of red suit) = P (E) = 2/52 = 1/26
(ii) Let E be the event of drawing a face card
The favourable outcomes are: 4 cards of jack, 4 cards of queen and 4 cards of king
Then, the numbers of favourable outcomes are = 12
∴ P (face card) = P (E) = 12/52 = 6/26 = 3/13
(iii) Let E be the event of drawing a red face card
The favourable outcomes are: 2 red cards of jack, 2 red cards of queen and 2 red cards of king
The number of favourable outcomes = 6
∴ P (red face card) = P (E) = 6/52 = 3/26
(iv) Let E be the favourable event of drawing a queen of black suit
The numbers of favourable outcomes are: 2
∴ P (black suit queen) = P (E) = 2/52 = 1/26
(v) Let E be the event of drawing a jack of heart
The number of favourable outcome is: 1
∴ P (jack of heart) = P (E) = 1/52
(vi) Let E be the event of drawing a spade
The numbers of favourable outcomes are: 13
∴ P (spade) = P (E) = 13/52 = 1/4