#### Chapters

Chapter 2: Exponents of Real Numbers

Chapter 3: Rationalisation

Chapter 4: Algebraic Identities

Chapter 5: Factorisation of Algebraic Expressions

Chapter 6: Factorisation of Polynomials

Chapter 7: Linear Equations in Two Variables

Chapter 8: Co-ordinate Geometry

Chapter 9: Introduction to Euclid’s Geometry

Chapter 10: Lines and Angles

Chapter 11: Triangle and its Angles

Chapter 12: Congruent Triangles

Chapter 13: Quadrilaterals

Chapter 14: Areas of Parallelograms and Triangles

Chapter 15: Circles

Chapter 16: Constructions

Chapter 17: Heron’s Formula

Chapter 18: Surface Areas and Volume of a Cuboid and Cube

Chapter 19: Surface Areas and Volume of a Circular Cylinder

Chapter 20: Surface Areas and Volume of A Right Circular Cone

Chapter 21: Surface Areas and Volume of a Sphere

Chapter 22: Tabular Representation of Statistical Data

Chapter 23: Graphical Representation of Statistical Data

Chapter 24: Measures of Central Tendency

Chapter 25: Probability

#### RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

## Chapter 25: Probability

#### Chapter 25: Probability Exercise 25.1 solutions [Pages 13 - 15]

A coin is tossed 1000 times with the following frequencies:

Head: 455, Tail: 545

Compute the probability for each event.

Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:

Two heads: 95 times

One tail: 290 times

No head: 115 times

Find the probability of occurrence of each of these events.

Three coins are tossed simultaneously 100 times with the following frequencies of different outcomes:

Outcome: | No head | One head | Two heads | Three heads |

Frequency: | 14 | 38 | 36 | 12 |

If the three coins are simultaneously tossed again, compute the probability of:

(i) 2 heads coming up.

(ii) 3 heads coming up.

(iii) at least one head coming up.

(iv) getting more heads than tails.

(v) getting more tails than heads.

1500 families with 2 children were selected randomly and the following data were recorded:

Number of girls in a family | 0 | 1 | 2 |

Number of families | 211 | 814 | 475 |

(i) No girl

(ii) 1 girl

(iii) 2 girls

(iv) at most one girl

(v) more girls than boys

In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays.

(i) he hits boundary

(ii) he does not hit a boundary.

The percentage of marks obtained by a student in monthly unit tests are given below:

Unit test: | I | II | III | IV | V |

Percentage of marks obtained: | 69 | 71 | 73 | 68 | 76 |

Find the probability that the student gets:

(i) more than 70% marks

(ii) less than 70% marks

(iii) a distinction

To know the opinion of the students about Mathematics, a survey of 200 students was conducted. The data is recorded in the following table:

Opinion: | Like | Dislike |

Number of students: | 135 | 65 |

Find the probability that a student chosen at random (i) likes Mathematics (ii) does not like it.

The blood groups of 30 students of class IX are recorded as follows:

A | B | O | O | AB | O | A | O | B | A | O | B | A | O | O |

A | AB | O | A | A | O | O | AB | B | A | O | B | A | B | O |

(i) A

(ii) B

(iii) AB

(iv) O

Eleven bags of wheat flour, each marked 5 Kg, actually contained the following weights of flour (in kg):

4.97, 5.05, 5.08, 5.03, 5.00, 5.06, 5.08, 4.98, 5.04, 5.07, 5.00

Find the probability that any of these bags chosen at random contains more than 5 kg of flour.

Following table shows the birth month of 40 students of class IX.

Jan | Feb | March | April | May | June | July | Aug | Sept | Oct | Nov | Dec |

3 | 4 | 2 | 2 | 5 | 1 | 2 | 5 | 3 | 4 | 4 | 4 |

Given below is the frequency distribution table regarding the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days.

Conc. of SO_{2} |
0.00-0.04 | 0.04-0.08 | 0.08-0.12 | 0.12-0.16 | 0.16-0.20 | 0.20-0.24 |

No. days: | 4 | 8 | 9 | 2 | 4 | 3 |

Find the probability of concentration of sulphur dioxide in the interval 0.12-0.16 on any of these days.

A company selected 2400 families at random and survey them to determine a relationship between income level and the number of vehicles in a home. The information gathered is listed in the table below:

Monthly income: (in Rs) |
Vehicles per family | |||

0 |
1 |
2 |
Above 2 | |

Less than 7000 7000-10000 10000-13000 13000-16000 16000 or more |
10 0 1 2 1 |
160 305 535 469 579 |
25 27 29 29 82 |
0 2 1 25 88 |

If a family is chosen, find the probability that family is:

(i) earning Rs10000-13000 per month and owning exactly 2 vehicles.

(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs 7000 per month and does not own any vehicle.

(iv) earning Rs 13000-16000 per month and owning more than 2 vehicle.

(v) owning not more than 1 vehicle

(vi) owning at least one vehicle.

The following table gives the life time of 400 neon lamps:

Life time (in hours) |
300-400 | 400-500 | 500-600 | 600-700 | 700-800 | 800-900 | 900-1000 |

Number of lamps: | 14 | 56 | 60 | 86 | 74 | 62 | 48 |

A bulb is selected of random, Find the probability that the the life time of the selected bulb is:

(i) less than 400

(ii) between 300 to 800 hours

(iii) at least 700 hours.

Given below is the frequency distribution of wages (in Rs) of 30 workers in a certain factory:

Wages (in Rs) | 110-130 | 130-150 | 150-170 | 170-190 | 190-210 | 210-230 | 230-250 |

No. of workers | 3 | 4 | 5 | 6 | 5 | 4 | 3 |

A worker is selected at random. Find the probability that his wages are:

(i) less than Rs 150

(ii) at least Rs 210

(iii) more than or equal to 150 but less than Rs 210.

#### Chapter 25: Probability solutions [Page 16]

Define a trial.

Define an elementary event.

Define an event.

Define probability of an event.

A big contains 4 white balls and some red balls. If the probability of drawing a white ball from the bag is `2/5`, find the number of red balls in the bag.

A die is thrown 100 times. If the probability of getting an even number is `2/5` . How many times an odd number is obtained?

Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes:

Outcome | 3 heads | 2 heads | 1 head | No head |

Frequency | 23 | 72 | 77 | 28 |

Find the probability of getting at most two heads.

what is the probability of getting at least two heads?

#### Chapter 25: Probability solutions [Pages 16 - 17]

Mark the correct alternative in each of the following:

The probability of an impossible event is

1

0

less than 0

greater than 1

The probability of a certain event is

0

1

greater than 1

less than 0

The probability an event of a trial is

1

0

less than 1

more than 1

Which of the following cannot be the probability of an event?

`1/3`

`3/5`

`5/3`

1

Two coins are tossed simultaneously. The probability of getting atmost one head is

`1/4`

`3/4`

`1/2`

`1/4`

A coin is tossed 1000 times, if the probability of getting a tail is 3/8, how many times head is obtained?

525

375

625

725

A dice is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below:

Outcome | 1 | 2 | 3 | 4 | 5 | 6 |

Frequency | 200 | 30 | 120 | 100 | 50 | 100 |

The probability of getting a prime number is

`1/3`

`2/3`

`49/60`

`39/125`

The percentage of attendance of different classes in a year in a school is given below:

Class: |
X | IX | VIII | VII | VI | V |

Attendance: | 30 | 62 | 85 | 92 | 76 | 55 |

What is the probability that the class attendance is more than 75%?

`1/6`

`1/3`

`5/6`

`1/2`

A bag contains 50 coins and each coin is marked from 51 to 100. One coin is picked at random. The probability that the number on the coin is not a prime number, is

`1/5`

`3/5`

`2/5`

`4/5`

In a football match, Ronaldo makes 4 goals from 10 penalty kicks. The probability of converting a penalty kick into a goal by Ronaldo, is

`1/4`

`1/6`

`1/3`

`2/5`

## Chapter 25: Probability

#### RD Sharma Mathematics Class 9 by R D Sharma (2018-19 Session)

#### Textbook solutions for Class 9

## RD Sharma solutions for Class 9 Mathematics chapter 25 - Probability

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Concepts covered in Class 9 Mathematics chapter 25 Probability are Probability - an Experimental Approach.

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