NCERT Solutions Class 9th Maths Chapter – 15 Probability Ex 15.1

Ncert Solutions Class 9th Maths (Chapter – 15) Exercise – 15.1 Question No. 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: 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:

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:

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 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 ₹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 Solution Class 9th Maths (Chapter – 15) Exercise – 15.1 Question No. 6

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.

Solution:

Total number of students = 90

(i) Number of students who obtained less than 20% in the mathematics test = 7
the probability that a student obtained less than 20% in the mathematics test = 7/90

(ii) Number of students who obtained marks 60 or above = 15 + 8 = 23
the probability that a student obtained marks 60 or above = 23/90

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.

Find the probability that a student chosen at random

(i) likes statistics, (ii) does not like it.

Solution: Total number of students = 135 + 65 = 200
(i) Number of students who like statistics = 135
the probability that a student likes statistics = 135/200 = 27/40

(ii) Number of students who do not like statistics = 65
the probability that a student does not like statistics = 65/200 = 13/40

Ncert Solutions Class 9th Maths (Chapter – 15) Exercise – 15.1 Question No. 9

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.

Solution: Lets assume a case :-
Number of 2 wheelers passed = 45
Number of 3 wheelers passed = 15
Number of 4 wheelers passed = 40
The time interval is 15 minutes for all the 3 conditions.
Total number of vehicles passed = Number of 2 wheelers + Number of 3 wheelers + Number of 4 wheelers
= 45 + 15 + 40 = 100
Probability that one vehicle out of total vehicles is 2 wheelers
= 45/100
= 9/20

Ncert Solutions Class 9th Maths (Chapter – 15) Exercise – 15.1 Question No. 10

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: Let’s assume these values
Let number of Classmates be 20
And numbers written by them are
123, 374, 223, 911, 121, 363, 542, 413, 821, 736, 417, 163, 616, 637, 275, 615, 522, 314, 716, 946
So, Total numbers written = 20
Now, we know that
Number is divisible by 3 if its sum of digits are divisible by 3
Here,
Numbers divisible by 3 are: 123, 363, 417, 615, 522
Now,
We need to find Probability that number is divisible by 3
Probability that number is divisible by 3 = Number of numbers divisible by 3/ Total numbers
= 5/20
= 1/4