#### Chapters

Chapter 2: Polynomials

Chapter 3: Coordinate Geometry

Chapter 4: Linear Equations in two Variables

Chapter 5: Introduction to Euclid's Geometry

Chapter 6: Lines and Angles

Chapter 7: Triangles

Chapter 8: Quadrilaterals

Chapter 9: Areas of Parallelograms and Triangles

Chapter 10: Circles

Chapter 11: Constructions

Chapter 12: Heron's Formula

Chapter 13: Surface Area and Volumes

Chapter 14: Statistics

Chapter 15: Probability

#### NCERT Mathematics Class 9

## Chapter 15 : Probability

#### Pages 284 - 285

In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did not hit a boundary.

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

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

Number of families | 475 | 814 | 211 |

Compute the probability of a family, chosen at random, having

(i) 2 girls (ii) 1 girl (iii) No girl

Also check whether the sum of these probabilities is 1.

In a particular section of Class IX, 40 students were asked about the months of their birth and the following graph was prepared for the data so obtained:-

Find the probability that a student of the class was born in August.

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 |

If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.

An organization selected 2400 families at random and surveyed them to determine a relationship between income level and the number of vehicles in a family. The information gathered is listed in the table below:-

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

0 | 1 | 2 | Above 2 | |

Less than 7000 | 10 | 160 | 25 | 0 |

7000 – 10000 | 0 | 305 | 27 | 2 |

10000 – 13000 | 1 | 535 | 29 | 1 |

13000 – 16000 | 2 | 469 | 59 | 25 |

16000 or more | 1 | 579 | 82 | 88 |

Suppose a family is chosen, find the probability that the family chosen is

(i) earning Rs 10000 − 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 vehicles.

(v) owning not more than 1 vehicle.

A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, she found that a few students got under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 − 20, 20 − 30… 60 − 70, 70 − 100. Then she formed the following table:-

Marks | Number of students |

0 - 20 | 7 |

20 - 30 | 10 |

30 - 40 | 10 |

40 - 50 | 20 |

50 - 60 | 20 |

60 - 70 | 15 |

70 - above | 8 |

Total 90 |

(i) Find the probability that a student obtained less than 20 % in the mathematics test.

(ii) Find the probability that a student obtained marks 60 or above.

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

Opinion | Number of students |

like | 135 |

dislike | 65 |

Find the probability that a student chosen at random

(i) likes statistics, (ii) does not like it

The distance (in km) of 40 engineers from their residence to their place of work were found as follows.

5 | 3 | 10 | 20 | 25 | 11 | 13 | 7 | 12 | 31 |

19 | 10 | 12 | 17 | 18 | 11 | 32 | 17 | 16 | 2 |

7 | 9 | 7 | 8 | 3 | 5 | 12 | 15 | 18 | 3 |

12 | 14 | 2 | 9 | 6 | 15 | 15 | 7 | 6 | 12 |

What is the empirical probability that an engineer lives:-

(i) less than 7 km from her place of work?What is the empirical probability that an engineer lives:

(ii) more than or equal to 7 km from her place of work?

(iii) within 1/2 km from her place of work?

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.

Concentration of SO_{2} (in ppm) |
Number of days (Frequency) |

0.00 − 0.04 | 4 |

0.04 − 0.08 | 9 |

0.08 − 0.12 | 9 |

0.12 − 0.16 | 2 |

0.16 − 0.20 | 4 |

0.20 − 0.24 | 2 |

Total | 30 |

The above frequency distribution table represents the concentration of sulphur dioxide in the air in parts per million of a certain city for 30 days. Using this table, find the probability of the concentration of sulphur dioxide in the interval 0.12 − 0.16 on any of these days.

Blood Group |
Number of Students |

A | 9 |

B | 6 |

AB | 3 |

O | 12 |

Total | 30 |

The above frequency distribution table represents the blood groups of 30 students of a class. Use this table to determine the probability that a student of this class, selected at random, has blood group AB.

#### NCERT Mathematics Class 9

#### Textbook solutions for Class 9

## NCERT solutions for Class 9 Mathematics chapter 15 - Probability

NCERT solutions for Class 9 Maths chapter 15 (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 Textbook for Class 9 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 9 Mathematics chapter 15 Probability are Probability - an Experimental Approach.

Using NCERT 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 NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 9 prefer NCERT Textbook Solutions to score more in exam.

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