# NCERT Solutions for Class 9 Maths Chapter 15 Probability| PDF Download

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**Chapter 15 Probability NCERT Solutions for Class 9 Maths**which will develop you understanding of the chapter and obtain maximum marks in the exams. These NCERT Solutions which are accurate and detailed and as per the latest syllabus released by CBSE. You can download PDF of Class 9 Maths Chapter 15 Probability NCERT Solutions make you able to solve the difficult problems in a exercise.Studyrankers experts have taken every while preparing these

**Chapter 15 Probability NCERT Solutions**that will develop your necessary skill to solve more and more questions. These NCERT Solutions will provide good experience and provide opportunities to learn new things.**Chapter 15 NCERT Solutions**help in solving the difficulties that lie ahead with ease.#### Page No: 283

**Exercise 15.1**

1. 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.

**Answer**

Total numbers of balls = 30

Numbers of boundary = 6

Numbers of time she didn't hit boundary = 30 - 6 = 24

Probability she did not hit a boundary = 24/30 = 4/5

2. 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 | Â Â Â Â Â Â 475Â Â Â Â Â Â | Â Â Â Â Â Â 814Â Â Â Â Â | Â Â Â Â Â 211 Â Â Â Â |

(i) 2 girlsÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â (ii) 1 girl Â Â Â Â Â Â Â Â Â (iii) No girl

Also check whether the sum of these probabilities is 1.

**Answer**

Total numbers of families = 1500

(i) Numbers of families having 2 girls = 475

Probability = Numbers of families having 2 girls/Total numbers of families

Â Â Â Â Â Â Â Â Â = 475/1500 = 19/60

(ii) Numbers of families having 1 girls = 814

Probability = Numbers of families having 1 girls/Total numbers of families

Â Â Â Â Â Â Â Â Â = 814/1500 = 407/750

Â (iii) Numbers of families having 2 girls = 211

Probability = Numbers of families having 0 girls/Total numbers of families

Â Â Â Â Â Â Â Â Â = 211/1500

Sum of the probability = 19/60 + 407/750Â + 211/1500

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = (475 + 814 + 211)/1500 = 1500/1500 = 1

Yes, the sum of these probabilities is 1.

3. Refer to Example 5, Section 14.4, Chapter 14. Find the probability that a student of the class was born in August.

**Answer**

Numbers of students = 6

Required probability = 6/40 = 3/20

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

OutcomeÂ Â Â Â Â Â Â | Â Â Â Â 3 headsÂ Â Â Â Â | Â Â Â Â 2 headsÂ Â Â Â | Â Â Â 1 headÂ Â Â | Â Â Â Â No headÂ Â Â Â Â |

Frequency | 23 | 72 | 77 | 28 |

**Answer**

Number of times 2 heads come up = 72

Total number of times the coins were tossed = 200

Required probability = 72/200 = 9/25

5. An organisation 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 â‚¹) |
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 â‚¹10000 â€“ 13000 per month and owning exactly 2 vehicles.(ii) earning â‚¹16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than â‚¹7000 per month and does not own any vehicle.

(iv) earning â‚¹13000 â€“ 16000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.

**Answer**

Total numbers of families = 2400

(i) Numbers of families earning â‚¹10000 â€“13000 per month and owning exactly 2 vehicles = 29

Required probability = 29/2400

(ii)Â Number of families earning â‚¹16000 or more per month and owning exactly 1 vehicle = 579

Required probability = 579/2400

(iii) Number of families earning less than â‚¹7000 per month and does not own any vehicle = 10 Required probability = 10/2400 = 1/240

(iv) Number of families earning â‚¹13000-16000 per month and owning more than 2 vehicles = 25

Required probability = 25/2400 = 1/96

(v) Number of families owning not more than 1 vehicle = 10+160+0+305+1+535+2+469+1+579

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â = 2062

Required probability = 2062/2400 = 1031/1200

Page No: 284

6. Refer to Table 14.7, Chapter 14.

(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.

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 |

**Answer**

Total numbers of students = 90

(i) Numbers of students obtained less than 20% in the mathematics test = 7

Required probability = 7/90

(ii) Numbers of student obtained marks 60 or above = 15+8 = 23

Required probability = 23/90

7. 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 |

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

**Answer**

Total numbers of students = 135 + 65 = 200

(i) Numbers of students who like statistics = 135

Required probability = 135/200 = 27/40

(ii) Numbers of students who does not like statistics = 65

Required probability = 65/200 = 13/40

8. Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives:

(i) less than 7 km from her place of work?

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

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

**Answer**

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

5Â Â Â Â 3 Â Â 10 Â Â 20 Â Â 25 Â Â 11 Â Â 13 Â Â 7 Â Â 12 Â Â 31Â Â Â Â 19Â Â Â Â 10 Â Â 12 Â Â 17 Â Â 18 Â Â Â 11 Â Â 3 Â Â Â 2 Â Â Â 17 Â Â Â Â 16 Â Â 2Â Â Â Â 7 Â Â 9Â Â Â Â 7Â Â Â Â 8 Â Â Â 3 Â Â 5 Â Â 12 Â Â 15 Â Â 18 Â Â 3Â Â Â Â 12Â Â Â Â 14 Â Â 2 Â Â 9 Â Â 6 Â Â 15 Â Â 15 Â Â 7 Â Â 6 Â Â 12

Total numbers of engineers = 40

(i) Numbers of engineers living less than 7 km from her place of work = 9

Required probability = 9/40

(ii) Numbers of engineers living less than 7 km from her place of work = 40 - 9 = 31

Required probability = 31/40

(iii) Numbers of engineers living less than 7 km from her place of work = 0

Required probability = 0/40 = 0

Page No: 285

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

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

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

**Answer**

Total numbers of bags = 11

Numbers of bags containing more than 5 kg of flour = 7

Required probability = 7/11

12. In Q.5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding 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.

The data obtained for 30 days is as follows:

0.03Â Â Â Â Â 0.08Â Â Â Â Â 0.08Â Â Â Â Â 0.09Â Â Â Â Â 0.04Â Â Â Â Â 0.17Â Â Â Â Â 0.16Â Â Â Â Â 0.05Â Â Â Â Â 0.02Â Â Â Â Â 0.06Â Â Â Â Â 0.18Â Â Â Â Â 0.20 Â Â Â 0.11Â Â Â Â 0.08Â Â Â Â Â 0.12 Â Â Â 0.13Â Â Â Â Â 0.22Â Â Â Â Â 0.07Â Â Â Â Â 0.08Â Â Â Â Â 0.01Â Â Â Â Â 0.10Â Â Â Â Â 0.06Â Â Â Â Â 0.09Â Â Â Â Â 0.18Â Â Â Â Â 0.11Â Â Â Â Â 0.07Â Â Â Â Â 0.05Â Â Â Â Â 0.07Â Â Â Â Â 0.01Â Â Â Â Â 0.04

**Answer**

Total numbers of days data recorded = 30 days

Numbers of days in which sulphur dioxide in the interval 0.12-0.16 = 2

Required probability = 2/30 = 1/15

13. In Q.1, Exercise 14.2, you were asked to prepare a frequency distribution table regarding 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.

The blood groups of 30 students of Class VIII 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.

**Answer**

Total numbers of students = 30

Numbers of students having blood group AB = 3

Required probability = 3/30 = 1/10

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## NCERT Solutions for Class 9 Maths Chapter 15 Probability

**Chapter 15 Probability Class 9 Maths NCERT Solutions**is good way through which one can build their basic knowledge. The numerical measure of uncertainty of an activity is called probability. The words â€˜doubtâ€™, â€˜chancesâ€™, â€˜most probablyâ€™ etc., show uncertainty or probability of happening of an action or activity.

â€¢ Probability â€“ an Experimental Approach: A trial is an action which results in one or several outcomes. An event for an experiment is the collection of some outcomes of the experiment. Let n be the total number of trials. The empirical probability P(E) of an event E happening, is given by

P(E) = Number of trials in which the event happened/The total number of trials.

Only one exercise is present in the

**chapter 15 NCERT Solutions**. We have also provided exercise wise solutions of every problem that you can find below.You will get

**accurate and detailed NCERT Solutions of Class 9 Maths**prepared by Studyrankers experts that can help in easily understand even the most difficult problems. You will be able to solve the difficult problems given in a exercise.### NCERT Solutions for Class 9 Maths Chapters:

**FAQ onÂ**

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**15 Probability**

#### What are the benefits of NCERT Solutions for Chapter 15 Probability Class 9 NCERT Solutions?

What are the benefits of NCERT Solutions for Chapter 15 Probability Class 9 NCERT Solutions?

Chapter 15 Probability NCERT Solutions that are very helpful in building your basic concepts embedded in the chapter. It is also very helpful in developing your problem solving skills.

#### What do you mean by random experiment?

What do you mean by random experiment?

An experiment in which all possible outcomes are known and the exact outcome cannot be predicted in advance, is called a random experiment.

#### What is uncertainty in Probability?

What is uncertainty in Probability?

A doubtful situation of an action or activity that may or may not take place, is called â€˜uncertaintyâ€™.

#### A coin is thrown once. Find the probability of getting a head.

A coin is thrown once. Find the probability of getting a head.

Number of possible outcomes = 2

Number of favourable outcome = 1

âˆ´ The required probability = (1/2).