(i) a spade

Total numbers of cards are 52

Total number of spade cards = 13

Probability of getting spade is = \(\frac{Total\,number\,of\,spade\,cards}{Total\,number\,of\,cards}\) = \(\frac{13}{52}\) = \(\frac{1}{4}\)

(ii) a black card

Total numbers of cards are 52

Cards of spades and clubs are black cards.

Number of spades = 13

Number of clubs = 13

Therefore, total number of black card out of 52 cards = 13 + 13 = 26

Probability of getting black cards is = \(\frac{Total\,number\,of\,black\,cards}{Total\,number\,of\,cards}\) = \(\frac{26}{52}=\frac{1}{2}\) 

(iii) the seven of clubs

Total numbers of cards are 52

Number of the seven of clubs cards = 1

Probability of getting the seven of clubs cards is = \(\frac{Total\,number\,of\,the\,seven\,of\,clubs\,cards}{Total\,number\,of\,cards}\)

= \(\frac{1}{52}\)

(iv) jack

Total numbers of cards are 52

Number of jack cards = 4

Probability of getting jack cards is = \(\frac{Total\,number\,of\,jack\,cards}{Total\,number\,of\,cards}\) = \(\frac{4}{52}=\frac{1}{13}\)

(v) the ace of spades

Total numbers of cards are 52

Number of the ace of spades cards = 1

Probability of getting ace of spades cards is = \(\frac{Total\,number\,of\,ace\,of\,spade\,cards}{Total\,number\,of\,cards}\) 

= \(\frac{1}{52}=\frac{1}{52}\)