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

(i) a black king


(ii) either a black card or a king


(iii) black and a king


(iv) a jack, queen or a king


(v) neither a heart nor a king


(vi) spade or an ace


(vii) neither an ace nor a king


(viii) neither a red card nor a queen


(ix) other than an ace


(x) a ten


(xi) a spade


(xii) a black card


(xiii) the seven of clubs


(xiv) jack


(xv) the ace of spades


(xvi) a queen


(xvii) a heart


(xviii) a red card

(i) a black king


Total numbers of cards are 52


Number of black king cards = 2


Probability of getting black king cards is =


Therefore Probability of getting black king cards is


(ii) either a black card or a king


Total numbers 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 =


Therefore Probability of getting either a black card or a king is


(iii) black and a king


Total numbers of cards are 52


Number of black and a king = 2


Probability of getting black and a king is =


Therefore Probability of getting black and a king is


(iv) a jack, queen or a king


Total numbers of cards are 52


Number of a jack, queen or a king = 12


Probability of getting a jack, queen or a king is =


Therefore Probability of getting a jack, queen or a king is


(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 king cards = 4


Probability of getting a king is =


Total probability of getting a heart and a king =


Therefore probability of getting neither a heart nor a king =


(vi) spade or an ace


Total numbers of cards are 52


Number of spade cards = 13


Probability of getting spade cards is =


Total numbers of cards are 52


Number of ace cards = 4


Probability of getting ace cards is =


Probability of getting ace and spade cards is =


Probability of getting an ace or spade cards is =


Therefore Probability of getting an ace or spade cards is =


(vii) 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 =


Therefore Probability of getting neither an ace nor a king is =


(viii) 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 52 cards = 13


Number of diamonds in a deck 52 cards = 13


Number of queen in a deck 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 =


Therefore Probability of getting neither a king nor a queen is =


(ix) 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 =


(x) a ten


Total numbers of cards are 52


Total number of ten cards = 4


Probability of getting non-ace is =


(xi) a spade


Total numbers of cards are 52


Total number of spade cards = 13


Probability of getting spade is =


(xii) 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 =


(xiii) 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 =


(xiv) jack


Total numbers of cards are 52


Number of jack cards = 4


Probability of getting jack cards is =


(xv) 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 =


(xvi) a queen


Total numbers of cards are 52


Number of queen cards = 4


Probability of getting queen cards is =


(xvii) a heart


Total numbers of cards are 52


Number of heart cards = 13


Probability of getting queen cards is =


(xviii) a red card


Total numbers of cards are 52


Number of red cards = 13+13 = 26


Probability of getting queen cards is =


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