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RD Sharma Solutions Class 8 Mathematics Solutions for Data Handling Probability Exercise 26.1 in Chapter 26 - Data Handling Probability
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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) 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 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
(vi) 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
(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 = 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
(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 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
(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 = Total number of non-ace cards/Total number of cards
= 48/52
= 12/13
∴ Probability of getting non-ace card is 12/13
(x) 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
(xi) A spade
Total numbers of cards are 52 Total number of spade cards = 13
Probability of getting spade is = Total number of spade cards/Total number of cards
= 13/52
= 1/4
∴ Probability of getting a spade is 1/4
(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
Total number of black card out of 52 cards = 13 + 13 = 26
Probability of getting black cards is = Total number of black cards/Total number of cards
= 26/52
= 1/2
∴ Probability of getting a black card is 1/2
(xiii) The seven of clubs Total numbers of cards are 52
Total number of the seven of clubs cards = 1
Probability of getting the seven of clubs cards is = Total number of the seven of club cards/ Total numbers of cards
= 1/52
∴ Probability of the seven of club card is 1/52
(xiv) Jack
Total numbers of cards are 52 Total number of jack cards = 4
Probability of getting jack cards is = Total number of jack cards/ Total numbers of cards
= 4/52
= 1/13
∴ Probability of the jack card is 1/13
(xv) The ace of spades
Total numbers of cards are 52
Total number of the ace of spades cards = 1
Probability of getting ace of spade cards is = Total number of ace of spade cards/ Total numbers of cards
= 1/52
∴ Probability of the ace of spade card is 1/52
(xvi) A queen
Total numbers of cards are 52 Total number of queen cards = 4
Probability of getting queen cards is = Total number of queen cards/Total numbers of cards
= 4/52
= 1/13
∴ Probability of a queen card is 1/13
(xvii) A heart
Total numbers of cards are 52 Total number of heart cards = 13
Probability of getting queen cards is = Total number of heart cards/Total numbers of cards
= 13/52
= 1/4
∴ Probability of a heart card is 1/4
(xviii) A red card
Total numbers of cards are 52
Total number of red cards = 13+13 = 26
Probability of getting queen cards is = Total number of red cards/Total numbers of cards
= 26/52
= 1/2 ∴ Probability of a red card is 1/2
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