#### 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

## Chapter 25: Probability

### RD Sharma solutions for Mathematics for Class 9 Chapter 25 Probability Exercise 25.1 [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.

### RD Sharma solutions for Mathematics for Class 9 Chapter 25 Probability [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?

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

RD Sharma solutions for Mathematics for Class 9 chapter 25 (Probability) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Mathematics for Class 9 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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

Using RD Sharma Class 9 solutions Probability exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer RD Sharma Textbook Solutions to score more in exam.

Get the free view of chapter 25 Probability Class 9 extra questions for Mathematics for Class 9 and can use Shaalaa.com to keep it handy for your exam preparation