Question

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 Select the correct answer from above options

Answer 1

(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