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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 |
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
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.
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-
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
5. An organisation selected 2400 families at random and sur-veyed them to determine a relationship between income level and the number of vehicles in a family. The infor-mation gathered is listed in the table below:
Suppose a family is chosen. Find the probability that the family chosen is
(i) earing Rs. 10000-13000 per month and owing exactly 2 vehicles.
(ii) earing Rs. 16000 or more per month and owing exactly 1 vehicle.
(iii) earing less than Rs. 7000 per month and does not own any vehicle.
(iv) earing 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 owing 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 owing 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
6. Refer to Table 14.7, chapter 14.
| Marks (out of 100) | 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 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 maths-ematics test = 7
Probability that a student obtained less than 20% in maths-
(ii) Number of students obtaining marks 60 or above =15+8 = 23
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
8. Refer to Q.2. Ex. 14.2
The distance (in km) of 40 female engineers from their resi-dence 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
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.
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 divis-ible by 3? Remember that a number is divisible by 3. if the sum of its digits is divisible by 3.
Ans: Students, do yourself.
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
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
13. In Q. 1, Exercise 14.2 given below, you were asked to prepare 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
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