(i) A black king

Total number of cards are 52

Number of black king cards = 2

Probability of getting black king cards is = Total number of black king cards/Total number of cards

= 2/52

= 1/26

∴ Probability of getting black king cards is 1/26

(ii) Either a black card or a king

Total number of cards are 52

Number of either a black card or a king = 28

Probability of getting either a black card or a king is = Total number of either black or king card/Total number of cards

= 28/52

= 7/13

∴ Probability of getting either a black card or a king is 7/13

(iii) Black and a king

Total number of cards are 52

Number of black and a king = 2

Probability of getting black and a king is = Total number of black and king card/Total number of cards

= 2/52

= 1/26

∴ Probability of getting black and a king is 1/26

(iv) a jack, queen or a king

Total number of cards are 52

Number of a jack, queen or a king = 12

Probability of getting a jack, queen or a king is = Total number of jack, queen or king card/Total number of cards

= 12/52

= 3/13

∴ Probability of getting a jack, queen or a king is 3/13

(v) Neither a heart nor a king

Total numbers of cards are 52

Total number of heart cards = 13

Probability of getting a heart is = Total number of hearts/Total number of cards

= 13/52

= 1/4

Total number of king cards = 4

Probability of getting a king is = Total number of king card/Total number of cards

= 4/52

= 1/13

Total probability of getting a heart and a king = 13/52 + 4/52 – 1/52

= (13+4-1)/52

= 16/52

= 4/13

∴ Probability of getting neither a heart nor a king = 1 – 4/13 = (13-4)/13 = 9/13