(i) Total number cards in a deck = 52 

Number of kings in a deck of cards = 4

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of drawing a king from the deck of cards P(king)

= \(\frac{Number\,of\,kings\,in\,a\,deck\,of\,cards}{Total\,number\,of\,cards\,in\,a\,deck}\) = \(\frac{4}{52}=\frac{1}{13}\)

(ii) Total number cards in a deck = 52 

Number of spades in a deck of cards = 13

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of drawing a spade from the deck of cards P(spade)

= \(\frac{Number\,of\,spades\,in\,a\,deck\,of\,cards}{Total\,number\,of\,cards\,in\,a\,deck}\) = \(\frac{13}{52}=\frac{1}{4}\)

(iii) Total number cards in a deck = 52

Chances of drawing a Red queen from the deck of cards = 2 (they are queen of hearts and queen of diamonds)

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of drawing a Red queen from the deck of cards P(Red queen)

= \(\frac{chances\,drawing\,a\,red\,queen\,from\,the\,deck\,of\,cards}{Total\,number\,of\,cards\,in\,a\,deck}\) = \(\frac{2}{52}=\frac{1}{26}\)

(iv) Total number cards in a deck = 52 

Chances of drawing a black 8 from the deck of cards = 2 (they are 8 of clubs and 8 of spades)

Probability (P) = \(\frac{Number\,of\,favorable\,outcomes}{Total\,number\,of\,outcomes}\)

∴ Probability of drawing a black 8 from a deck of cards P(black 8)

= \(\frac{chances\,drawing\,a\,black\,from\,from\,the\,deck\,of\,cards}{Total\,number\,of\,cards\,in\,a\,deck}\) = \(\frac{2}{52}=\frac{1}{26}\)