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
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
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
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 =
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 =
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 numbers of cards are 52
Total number of ten cards = 4
Probability of getting non-ace is =
Total numbers of cards are 52
Total number of spade cards = 13
Probability of getting spade is =
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 =
Total numbers of cards are 52
Number of the seven of clubs cards = 1
Probability of getting the seven of clubs cards is =
Total numbers of cards are 52
Number of jack cards = 4
Probability of getting jack cards is =
Total numbers of cards are 52
Number of the ace of spades cards = 1
Probability of getting ace of spades cards is =
Total numbers of cards are 52
Number of queen cards = 4
Probability of getting queen cards is =
Total numbers of cards are 52
Number of heart cards = 13
Probability of getting queen cards is =
Total numbers of cards are 52
Number of red cards = 13+13 = 26
Probability of getting queen cards is =