Total number of cards = 52. 

∴ Number of all possible outcomes in drawing a card at random = 52. 

i) Number of outcomes favourable to the king of red colour = 2(♥ K, ♦ K)

∴ Probability of getting the king of red colour

P(E) = \(\frac{No.\,of\,favourable\,outcomes}{Total\,no.\,of\,outcomes}\)

\(=\frac{2}{52}=\frac{1}{26}\)

ii) Number of face cards in a deck of cards = 4 × 3 = 12 (K, Q, J) 

Number of outcomes favourable to select a face card = 12. 

∴ Probability of getting a face card

= \(\frac{No.\,of\,favourable\,outcomes}{Total\,no.\,of\,outcomes}\)

\(=\frac{12}{52}=\frac{3}{13}\)

iii) Number of red face cards = 2 × 3 = 6. 

∴ Number of outcomes favourable to select a red face card = 6. 

∴ Probability of getting a red face

= \(\frac{No.\,of\,favourable\,outcomes}{Total\,no.\,of\,outcomes}\)

\(=\frac{6}{52}=\frac{3}{26}\)

iv) Number of outcomes favourable to the jack of hearts = 1. 

∴ Probability of getting jack of hearts

= \(\frac{No.\,of\,favourable\,outcomes}{Total\,no.\,of\,outcomes}\)

= \(\frac{1}{52}\)

v) Number of spade cards = 13 

∴ Number of outcomes favourable to ‘a spade card’ = 13. 

∴ Probability of drawing a spade

= \(\frac{No.\,of\,favourable\,outcomes}{Total\,no.\,of\,outcomes}\)

\(=\frac{13}{52}=\frac{1}{4}\)

vi) Number of outcomes favourable to the queen of diamonds = 1. 

∴ Probability of drawing the queen of diamonds

= \(\frac{No.\,of\,favourable\,outcomes}{Total\,no.\,of\,outcomes}\)

= \(\frac{1}{52}\)