A deck of playing cards has 52 cards.

Shuffling the deck properly and one card is drawn, then the total possible outcomes = 52.

(i) There are four jack in the deck of which the jack of hearts arid diamonds are red.

∴ The number of favourable outcomes of drawing a red jack = 2

∴ Probability that the card drawn is a red jack = \(\frac { 2 }{ 52 }\)

= \(\frac { 1 }{ 26 }\)

(ii) The deck contains 13 cards of hearts and 13 cards of diamonds. 

So the number of favourable outcomes that the card is red = 26.

∴ The probability that the card drawn is red 

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

(iii) There is only one hearts ace in the deck.

So, the number of favourable outcomes = 1

∴ The probability that the drawn card is a hearts ace = \(\frac { 1 }{ 52 }\)

(iv) There is only one diamonds queen in the deck,

So, the number of favourable outcomes of getting a diamond queen = 1

∴ The probability that the card drawn is a diamonds queen = \(\frac { 1 }{ 52 }\)

(v) There are 13 spades cards in the deck 

so, the favourable outcomes = 13

∴ The probability that the card drawn is a spades

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