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
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 SEBA Class 9 Mathematics Chapter 15 Probability Solutions for All Subject, You can practice these here.
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
