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Rd sharma solutions

CHAPTERS

6. Algebraic Expressions and Identities

8. Division of Algebraic Expressions

9. Linear Equation in One Variable

10. Direct and Inverse Variations

13. Profit Loss Discount and Value Added Tax

15. Understanding Shapes Polygons

16. Understanding Shapes Quadrilaterals

17. Understanding Shapes Special Types Quadrilaterals

20. Area of Trapezium and Polygon

21. Volume Surface Area Cuboid Cube

22. Surface Area and Volume of Right Circular Cylinder

23. Classification And Tabulation Of Data

24. Classification And Tabulation Of Data Graphical Representation Of Data As Histograms

25. Pictorial Representation Of Data As Pie Charts Or Circle Graphs

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

Algebraic Expressions and Identities

Division of Algebraic Expressions

Linear Equation in One Variable

Profit Loss Discount and Value Added Tax

Understanding Shapes Quadrilaterals

Understanding Shapes Special Types Quadrilaterals

Volume Surface Area Cuboid Cube

Surface Area and Volume of Right Circular Cylinder

Classification And Tabulation Of Data

Classification And Tabulation Of Data Graphical Representation Of Data As Histograms

Pictorial Representation Of Data As Pie Charts Or Circle Graphs

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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