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A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is:

(i) spade or an ace

(ii) neither an ace nor a king

(iii) neither a red card nor a queen

(iv) other than an ace

(v) a ten

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(i) Spade or an ace

Total numbers of cards are 52

Number of spade cards = 13

Probability of getting spade cards is = Total number of spade card/Total number of cards

= 13/52

Number of ace cards = 4

Probability of getting ace cards is = Total number of ace card/Total number of cards

= 4/52

= 1/13

Probability of getting ace and spade cards is = Total number of ace and spade card/Total number of cards

= 1/52

Probability of getting an ace or spade cards is = 13/52 + 4/52 – 1/52

= (13+4-1)/52

= 16/52

= 4/13

∴ Probability of getting an ace or spade cards is = 4/13

(ii) Neither an ace nor a king

Total numbers of cards are 52

Number of king cards = 4

Number of ace cards = 4

Total number of cards = 4 + 4 = 8

Total number of neither an ace nor a king are = 52 – 8 = 44

Probability of getting neither an ace nor a king is = Total number of neither ace nor king card/Total number of cards

= 44/52

= 11/13

∴ Probability of getting neither an ace nor a king is 11/13

(iii) Neither a red card nor a queen

Total numbers of cards are 52

Red cards include hearts and diamonds

Number of hearts in a deck of 52 cards = 13

Number of diamonds in a deck of 52 cards = 13

Number of queen in a deck of 52 cards = 4

Total number of red card and queen = 13 + 13 + 2 = 28 [since queen of heart and queen of diamond are removed]

Number of card which is neither a red card nor a queen = 52 – 28 = 24

Probability of getting neither a king nor a queen is = Total number of neither red nor queen card/Total number of cards

= 24/52

= 6/13

∴ Probability of getting neither a king nor a queen is 6/13

(iv) Other than an ace

Total numbers of cards are 52

Total number of ace cards = 4

Total number of non-ace cards = 52-4 = 48

Probability of getting non-ace is = Total number of non-ace cards/Total number of cards

= 48/52

= 12/13

∴ Probability of getting non-ace card is 12/13

(v) A ten

Total numbers of cards are 52

Total number of ten cards = 4

Probability of getting ten cards is = Total number of ten cards/Total number of cards

= 4/52

= 1/13

∴ Probability of getting ten card is 1/13

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