NCERT Solutions for Chapter 15 Probability Class 9 Maths
Chapter Name | NCERT Solutions for Chapter 15 Probability |
Class | Class 9 |
Topics Covered |
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Related Study Materials |
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Short Revision for Ch 15 Probability Class 9 Maths
- The experimental probability of an even E is written as P(E).
- P(E) = (Number of trials in which E has happened)/Total number of trials
- The probability of a sure event is 1.
- The probability of an impossible event is 0.
- The probability of an event lies between 0 and 1 (both included).
- On throwing a coin, the probability of getting a head is 1/2.
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.
Solution
Total number of balls = 30.
Number of hitting the boundary = 6.
Number of balls when boundary is not hit = 30 - 6 = 24.
Probability that she did not hit the 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 | 475 | 814 | 211 |
(i) 2 girls (ii) 1 girl (iii) No girl
Also check whether 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.
Number of students born in August = 6.
∴ Probability that a student was born in August = 6/40 = 3/20 .
4. 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 |
∴ Probability of 2 heads coming up = 72/200 = 9/25.
If the three coins are simultaneously tossed again, then the probability will be the same.
Hence, the required probability is 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 ₹) |
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 |
(i) earning ₹10000 – 13000 per month and owning exactly 2 vehicles.
(ii) earning ₹16000 or more per month and owning exactly 1 vehicle.
(iii) earning less than ₹7000 per month and does not own any vehicle.
(iv) earning ₹13000 – 16000 per month and owning more than 2 vehicles.
(v) owning not more than 1 vehicle.
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.
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.
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 ½ km from her place of work?
Solution
Total number of engineers = 40
(i) Number of engineers having distance of less than 7 km from their residence to the place of work = 9.
∴ Probability that an engineer lives less than 7 km from her place of work = 9/40.
(ii) Number of engineers having distance of more than or equal to 7 km from their residence to the place of work = 40 - 9 = 31.
∴ Probability that an engineer lives more than or equal to 7 km from her place of work = 31/40
(iii) There is no engineer within 1/2 km from her place of work.
∴Probability that an engineer lives within 1/2 km from her place of work = 0.
9. Activity : Note the frequency of two-wheelers, three-wheelers 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.
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.
Solution
We know that there is one number among three consecutive positive integers is divisible by 3. Hence, about one third of the students of the class would write the numbers divisible by 3.
Hence, the required probability is 1/3.
Note : Here we are assuming number of students in class is a multiple of 3.
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 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.
Solution
Total number of bags is 11.
Number of bags containing flour (in kg) more than 5 kg is 7, i.e., 5.05, 5.08, 5.03, 5.06, 5.08, 5.04, 5.07.
∴ Probability that a bag chosen at random contains more than 5 kg of flour = 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:
0.03 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 0.04
Solution
From the table, we notice that on two days out of 30, the concentration of sulphur dioxide (in ppm) was in the interval 0.12 - 0.16.
∴ Probability of concentration of sulphur dioxide in the interval 0.12 - 0.16 on any day selected = 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.
Solution
From the given table, we notice there are 3 students with blood group AB out of 30 students.
∴ Probability that a student selected has blood group AB = 3/30 = 1/10.