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NCERT Class 9 Maths Textbook Chapter 15 With Answer Book PDF Free Download
Chapter 15: Probability
15.1 Introduction
In everyday life, we come across statements such as
(1) It will probably rain today.
(2) I doubt that he will pass the test.
(3) Most probably, Kavita will stand first in the annual examination.
(4) Chances are high that the prices of diesel will go up.
(5) There is a 50-50 chance of India winning a toss in today’s match.
The words ‘probably’, ‘doubt’, ‘most probably’, ‘chances’, etc., used in the statements above involve an element of uncertainty. For example, in (1), ‘probably rain’ will mean it may rain or may not rain today.
We are predicting rain today based on our past experience when it rained under similar conditions. Similar predictions are also made in other cases listed in (2) to (5).
15.2 Probability – an Experimental Approach
In earlier classes, you have had a glimpse of probability when you performed experiments like the tossing of coins, throwing of dice, etc., and observed their outcomes.
You will now learn to measure the chance of occurrence of a particular outcome in an experiment.
| Author | NCERT |
| Language | English |
| No. of Pages | 41 |
| PDF Size | 816 KB |
| Category | Mathematics |
| Source/ Credits | ncert.nic.in |
NCERT Solutions Class 9 Maths Chapter 15 Probability
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:
According to the question,
Total number of balls = 30
Numbers of boundary = 6
Number of time batswoman 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 | 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.
Solution:
Total numbers of families = 1500
(i) Numbers of families having 2 girls = 475
Probability = Numbers of families having 2 girls/Total numbers of families
= 475/1500 = 19/60
(ii) Numbers of families having 1 girl = 814
Probability = Numbers of families having 1 girl/Total numbers of families
= 814/1500 = 407/750
(iii) Numbers of families having 0 girls = 211
Probability = Numbers of families having 0 girls/Total numbers of families
= 211/1500
Sum of the probability = (19/60)+(407/750)+(211/1500)
= (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.
Solution:
Total numbers of students in the class = 40
Numbers of students born in August = 6
The probability that a student of the class 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 |
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
Solution:
Number of times 2 heads come up = 72
Total number of times the coins were tossed = 200
∴, the probability of 2 heads coming up = 72/200 = 9/25
5. An organization 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 |
Suppose a family is chosen. Find the probability that the family chosen is
(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.
Solution:
Total number of families = 2400
(i) Numbers of families earning ₹10000 –13000 per month and owning exactly 2 vehicles = 29
∴, the probability that the family chosen is earning ₹10000 – 13000 per month and owning exactly 2 vehicles = 29/2400
(ii) Number of families earning ₹16000 or more per month and owning exactly 1 vehicle = 579
∴, the probability that the family chosen is earning₹16000 or more per month and owning exactly 1 vehicle = 579/2400
(iii) Number of families earning less than 7000 per month and does not own any vehicle = 10
∴, the probability that the family chosen is earning less than ₹7000 per month and does not own any vehicle = 10/2400 = 1/240
(iv) Number of families earning ₹13000-16000 per month and owning more than 2 vehicles = 25
∴, the probability that the family chosen is earning ₹13000 – 16000 per month and owning more than 2 vehicles = 25/2400 = 1/96
(v) Number of families owning not more than 1 vehicle = 10+160+0+305+1+535+2+469+1+579
= 2062
∴, the probability that the family chosen owns not more than 1 vehicle = 2062/2400 = 1031/1200
NCERT Class 9 Maths Textbook Chapter 15 With Answer Book PDF Free Download