**SEBA Class 9 Mathematics Chapter 15 Probability** **Solutions**, **SEBA Class 9 Maths Textbook Notes in English Medium, SEBA Class 9 Mathematics Chapter 15 Probability** **Solutions** in English to each chapter is provided in the list so that you can easily browse throughout different chapter Assam Board **SEBA Class 9 Mathematics Chapter 15 Probability** **Notes** and select needs one.

**SEBA Class 9 Mathematics Chapter 15 Probability**

**SEBA Class 9 Mathematics Chapter 15 Probability**Also, you can read the SCERT book online in these sections Solutions by Expert Teachers as per SCERT (CBSE) Book guidelines. **SEBA****Class 9 Mathematics Chapter 15 Probability Question Answer. **These solutions are part of SCERT All Subject Solutions. Here we have given

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**Solutions****SEBA Class 9 Mathematics Chapter 15 Probability****Probability**

**Probability****Chapter – 15**

Exercise 15.1 |

**Q.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.**

Ans: Let E be the event of hitting the boundary.

The,

∴ Probability of not hitting the boundary

= 1-Probability of hitting the boundary

= 1 – P(E) = 1 – 0.2 = 0.8

**Q.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 | 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.

Ans: Total number of families

= 475 + 814 + 211 = 1500

(i) Probability of a family, chosen at random, having 2 girls

(ii) Probability of a family, chosen at random, having 1 girl

(iii) Probability of a family, chosen at random, having no girl

Sum of these probabilities

Hence the sum is checked.

**Q.3. Refer to Example 5, section 14.4, Chapter 14. Find the prob- ability that a student of the class was born in August.**

**Or **

In a particular section of Class IX, 40 students were asked about the months of their birth, the fol- lowing graph was prepared for the data obtained.

Ans: Total number of students born in the year

= 3 + 4 + 2 + 2 + 5 + 1 + 2 + 6 + 3 + 4 + 4 + 4 = 40

Number of students born in August = 6

∴ Probability that a student of the class was born in Au-

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

Outcomes | 3 heads | 2 heads | 1 head | No head |

Frequency | 23 | 72 | 71 | 28 |

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

Ans: Total number of times the three coins are tossed = 200

Number of times when 2 heads appear = 72

**Q.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:**

**Suppose a family is chosen. Find the probability that the family chosen is**

**(i) earning Rs. 10000-13000 per month and owing exactly 2 vehicles.**

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

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

**(iv) earning Rs. 13000-16000 per month and owing more than 2 vehicles.**

**(v) owing not more than I vehicle.**

Ans: Total number of families selected – 2400

(i) Number of families earing Rs. 10000 -13000 per month and owing exactly 2 vehicles – 29

∴ Probability that the family chosen is earing Rs. 10000-

(ii) Number of families earing Rs. 16000 or more per month and owing exactly 1 vehicle 579

∴ Probability that the family chosen is earing Rs. 16000 or more per month and owing exactly 1 vehicle

(iii) Number of families earing less than Rs. 7000 per month and does not own any vehicle = 10

∴ Probability that the family chosen is earing less than Rs. 7000 per month and does not own any vehicle

(iv) Number of families earing Rs. 1300 -16000 per month and own more than 2 vehicles = 25

∴ Probability that the family chosen is earing Rs. 13000- 16000 per month and owing more than 2 vehicles

(v) Number of families owing not more than I vehicle = Number of families owing 0 vehicle + Number of fami- lies owning 1 vehicle

=(10+0+1+2+1)+(160+305+535+469+579)

= 14+2048-2062

∴ Probability that the family chosen owns not more than 1

**Q.6. Refer to Table 14.7, chapter 14.**

Marks (out of 100) | Number of Students |

0-20 | 7 |

20- | 10 |

30- | 10 |

40- | 20 |

50- | 20 |

60- | 15 |

70-above | 8 |

Total | 90 |

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

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

Ans: Total number of students = 90

(i) Number of students obtaining less than 20% in the mathematics test=7

Probability that a student obtained less than 20% in maths-

(ii) Number of students obtaining marks 60 or above =15+8=23

**Q.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 |

**Find the probability that a student student chosen at random**

(i) likes statistics,

(ii) does not like it.

Ans: Total number of students = 200

(i) Number of students who like statistics = 135

∴ Probability that a student chosen at random likes statistics

(ii) Number of students who do not like statistics = 65

∴ Probability that a student chosen at random does not like it

Aliter: Probability that a student chosen at random does like statistics

= 1-probability that a student chosen at random likes statistics

Exercise 15.2 |

**Q.8. The distance (in km) of 40 female 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 | 13 | 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?**

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

Ans: Total number of female engineers = 40

(i) Number of female engineers whose distance (in km) from their residence to their place of work is less than 7 km = 9

∴ Probability that an engineer lives less than 7 km from her

(ii) Number of female engineers whose distance (in km) from their residence to their place of work is more than or equal to

7 km = 31.

∴ Probability that an engineer lives more than or equal to 7 km

Aliter: Probability that an engineer lives more than or equal to 7 km from her place of residence.

= 1-probability that an engineer lives less than 7 km from her place work.

(iii) Number of female engineers whose distance (in km) from

**Q.9. Activity: Note the frequency of two wheelers, three wheel- ers and four wheelers going past during a time interval, in front of your school gate. Find the probability that any one vehicle out of the total vehicles you have observed is a two- wheeler.**

Ans: Students, do yourself.

**Q.10. Activity: Ask all the students in your class to write a 3-digit number. Choose any student from the room at random. What is the probability that the number written by her/him is divisible by 3? Remember that a number is divisible by 3. if the sum of its digits is divisible by 3.**

Ans: Students, do yourself.

**Q. 11. 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 5.04 5.07 5.00 **

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

Ans: Total number of bags of wheat flour = 11

Number of bags of wheat flour containing more than 5 kg of flour = 7

∴ Probability that any of the bags, chosen at random, contains

**Q.12. In Q. 5, Exercise 14.2 given below, you were asked to pre- pare a frequency distribution table, regarding the con- centration of sulphur dioxide in the air in parts per mil- lion 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.”A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows: 0.03 0.08 0.08 0.09 0.04 0.17 0.16 0.05**

**0.02 0.06 0.18 0.20 0.11 0.08 0.12 0.13 0.22 0.07 0.08 0.01 0.10 0.06 0.09 0.18**

**0.11 0.07 0.05 0.07 0.01 0.4”**

Ans: Total number of days=30

Number of days on which the concentration of sulphur diox- ide is in the interval 0.12 0.16-2

∴ Probability that the concentration of sulphur dioxide is in the

**Q.13. In Q. 1, Exercise 14.2 given below, you were asked to pre- pare a frequency distribution table regarding the blood groups of 30 students of a class. Use this table to deter- mine 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. **

Represent this data in the form of a frequency distribution table. Find out which is the most common and which is the rarest blood group among these students.”

Ans: Total number of students = 30

Number of student = 30

Number of students having blood groups AB = 3

∴ Probability that a student of this class, selected at ran- dom, has blood group