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Class 9th Science
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Class 9th Math
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Class 9 Social Science History: India and the Contemporary World â€“ I
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Class 9 Social Science Geography: Contemporary India â€“ I
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Class 9 Social Science Civics (Political Science): Democratic Politics â€“ I
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Class 9 Social Science Economics: Understanding Economic Development â€“ I
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Class 9 English Beehive
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Class 9 English Beehive Poem
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Class 9 English Moments
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Online Class For 9th Standard Students (CBSE) (English Medium)

### Exercise 15.1 Page: 283

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 didnâ€™t hit boundary = 30 â€“ 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 girlsÂ Â Â Â Â Â Â Â Â Â Â Â Â Â Â  (ii) 1 girl Â  Â  Â  Â  Â  Â  Â  Â  Â  (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

Â  Â  Â  Â  Â  Â  Â  Â  Â  = 475/1500 = 19/60

(ii) Numbers of families having 1 girls = 814

Probability = Numbers of families having 1 girls/Total numbers of families

Â  Â  Â  Â  Â  Â  Â  Â  Â  = 814/1500 = 407/750

(iii) Numbers of families having 2 girls = 211

Probability = Numbers of families having 0 girls/Total numbers of families

Â  Â  Â  Â  Â  Â  Â  Â  Â  = 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 = 72Â

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 Rs 10000 â€“ 13000 per month and owning exactly 2 vehicles.

(ii) earning Rs 16000 or more per month and owning exactly 1 vehicle.

(iii) earning less than Rs 7000 per month and does not own any vehicle.

(iv) earning Rs 13000 â€“ 16000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.Â

Solution:

Total number of families = 2400

(i) Numbers of families earning Rs 10000 â€“13000 per month and owning exactly 2 vehicles = 29

, the probability that the family chosen is earning Rs 10000 â€“ 13000 per month and owning exactly 2 vehicles = 29/2400

(ii) Number of families earning Rs 16000 or more per month and owning exactly 1 vehicle = 579

, the probability that the family chosen is earning Rs 16000 or more per month and owning exactly 1 vehicle = 579/2400

(iii) Number of families earning less than Rs 7000 per month and does not own any vehicle = 10

, the probability that the family chosen is earning less than Rs 7000 per month and does not own any vehicle = 10/2400 = 1/240

(iv) Number of families earning Rs 13000-16000 per month and owning more than 2 vehicles = 25

, the probability that the family chosen is earning Rs 13000 â€“ 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

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

### 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 Â˝ km from her place of work?

Solution:

The distance (in km) of 40 engineers from their residence to their place of work were found as follows:

5Â Â Â Â  3 Â  Â  10 Â  Â  20 Â  Â  25 Â  Â  11 Â  Â  13 Â  Â  7 Â  Â  12 Â  Â  31Â Â Â Â  19Â Â Â Â  10 Â  Â  12 Â  Â  17 Â  Â  18 Â  Â Â  11 Â  Â  3 Â  Â Â 2 Â

17 Â Â 16 Â  Â  2Â Â Â Â  7 Â  Â  9Â Â Â Â  7Â Â Â Â  8 Â  Â Â  3 Â  Â  5 Â  Â  12 Â  Â  15 Â  Â  18 Â  Â  3Â Â Â Â 12Â Â Â  14 Â  Â  2 Â  Â  9 Â  Â  6

15 Â  Â  15 Â  Â 7 Â  Â  6 Â  Â  12

Total numbers of engineers = 40

(i) Number of engineers living less than 7 km from their place of work = 9

,the probability that an engineer lives less than 7 km from her place of work = 9/40

(ii) Number of engineers living more than or equal to 7 km from their 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) Number of engineers living within Â˝ km from their place of work = 0

, the probability that an engineer lives within Â˝ km from her place of work = 0/40 = 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.

Solution:

The question is an activity to be performed by the students.

Hence, perform the activity by yourself and note down your inference.

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:

The question is an activity to be performed by the students.

Hence, perform the activity by yourself and note down your inference.

11. Eleven bags of wheat flour, each marked 5 kg, actually contained the following weights of flour (in kg):

4.97Â Â Â Â Â  5.05Â Â Â Â Â  5.08Â Â Â Â  5.03Â Â Â Â  5.00Â Â Â Â  5.06Â Â Â Â  5.08 Â  Â Â  4.98Â Â Â Â Â Â  5.04Â Â Â Â Â Â  5.07Â Â Â Â Â Â  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 present = 11

Number of bags containing more than 5 kg of flour = 7

, the probability that any of the bags chosen at random contains more than 5 kg of flour = 7/11

Class 9th maths chapter15

### 12. In Q.5, Exercise 14.2,

you were asked to prepare a frequency distribution table, regarding the concentration of ulphur 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 ulphur dioxide in the interval 0.12-0.16 on any of these days.

The data obtained for 30 days is as follows:
0.03Â Â Â Â Â  0.08Â Â Â Â Â  0.08Â Â Â Â Â  0.09Â Â Â Â Â  0.04Â Â Â Â Â  0.17Â Â Â Â Â  0.16Â Â Â Â Â  0.05Â Â Â Â Â  0.02Â Â Â Â Â  0.06Â Â Â Â Â  0.18Â Â Â Â Â  0.20 Â  Â Â  0.11Â Â Â  Â  0.08Â Â Â Â Â  0.12 Â  Â Â  0.13Â Â Â Â Â  0.22Â Â Â Â Â  0.07Â Â Â Â Â  0.08Â Â Â Â Â  0.01Â Â Â Â Â  0.10Â Â Â Â Â  0.06Â Â Â Â Â  0.09Â Â Â Â Â  0.18Â Â Â Â Â  0.11Â Â Â Â Â  0.07Â Â Â Â Â  0.05Â Â Â Â Â  0.07Â Â Â Â Â  0.01Â Â Â Â Â  0.04

Solution:

Total number of days in which the data was recorded = 30 days

Numbers of days in which ulphur dioxide was present in between the interval 0.12-0.16 = 2

, the probability of the concentration of ulphur dioxide in the interval 0.12-0.16 on any of these days = 2/30 = 1/15

Class 9th maths chapter15

### 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:

Total numbers of students = 30

Number of students having blood group AB = 3

, the probability that a student of this class, selected at random, has blood group AB = 3/30 = 1/10