NCERT Solutions for Exercise 15.1 Class 9 Maths Chapter 15 - Probability

Suppose a family is chosen. Find the probability that the family chosen is earning ` Rs. 10000 – Rs.13000 per month and owning exactly 2 vehicles.

Answer:

Although it is given that,

Total no. of families= 2400

Let us find this by adding all the cases

= 10+0+1+2+1+160+305+535+469+579+25+27+29+59+82+0+2+1+25+88 =2400

Earning Rs. 10000 – Rs.13000 per month and owning exactly 2 vehicles =29

P(Earning Rs. 10000–Rs.13000 per month and owning exactly 2 vehicles)= P ₁

P ₁ = 29/2400

Q5 (ii) 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

Suppose a family is chosen. Find the probability that the family chosen is earning Rs.16000 or more per month and owning exactly 1 vehicle.

Answer:

Although it is given that,

Total no. of families= 2400

Let us find by this adding all the cases

= 10+0+1+2+1+160+305+535+469+579+25+27+29+59+82+0+2+1+25+88 =2400

Total no. of families earning Rs.16000 or more per month and owning exactly 1 vehicle = 579

P(earning Rs.16000 or more per month and owning exactly 1 vehicle )= P2

P2 = 579/2400

Q5 (iii) 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:

Suppose a family is chosen. Find the probability that the family chose is earning less than Rs. 7000 per month and does not own any vehicle.

Answer:

Although it is given that,

Total no. of families= 2400

Let us find by this adding all the cases

= 10+0+1+2+1+160+305+535+469+579+25+27+29+59+82+0+2+1+25+88 =2400

Total no. of families, those are earning less than Rs. 7000 per month and not having any vehicle = 10

P(earning less than Rs. 7000 per month and does not have any vehicle)= P3

P3 = 10/2400

=1/240

Ans: 1/240

Q5 (iv) 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:

Suppose a family is chosen. Find the probability that the family chose is earning `Rs.13000 – 16000 per month and owning more than 2 vehicles.

Answer:

Although it is given that,

Total no. of families= 2400

Let us find by this adding all the cases

= 10+0+1+2+1+160+305+535+469+579+25+27+29+59+82+0+2+1+25+88 =2400

Total number of families,those are earning Rs.13000 – 16000 per month and owning more than 2 vehicles = 25

P(earning Rs.13000 – 16000 per month and owning more than 2 vehicles)= P4

P4 = 25/2400

=1/96

Ans :1/96

Q5 (v) 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:

Suppose a family is chosen. Find the probability that the family chosen is owning not more than 1 vehicle.

Answer:

Although it is given that,

Total no. of families= 2400

Let us find by this adding all the cases

= 10+0+1+2+1+160+305+535+469+579+25+27+29+59+82+0+2+1+25+88 =2400

Total number of families owning not more than 1 vehicle= 10+0+1+2+1+160+305+535+469+579 = 2062

Let, P(families owning not more than 1 vehicle)= P5

P5 = 2062/2400

Q6 (i) Refer to Table 14.7, Chapter 14. Find the probability that a student obtained less than 20% in the mathematics test.

Answer:

From the above question, the data of our interest is:

Total no. of students =90

Total no. of students who obtained less than 20% in the mathematics test= 7

P(student obtained less than 20% in the mathematics test) = 7/90

Ans: 7/90

Q6 (ii) Refer to Table 14.7, Chapter 14. Find the probability that a student obtained marks 60 or above.

Answer:

From the above question, the data of our interest is:

Total no. of students =90

Total no. of students who obtained marks 60 or above = 15+8 =23

P(a student obtains marks 60 or above) = 23/90

Ans: 23/90

Q7 (i) 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 is chosen at random likes statistics,

Answer:

From the above question, the data of our interest is:

Total no. of students =135+65 =200

Total no. of students who like statistics = 135

P(students like statistics )= 135/200 =27/40

Ans: 27/40

Q7 (ii) 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 does not like it.

Answer:

From the above question, the data of our interest is:

Total no. of students =135+65=200

Total no. of students who do not like it.= 65

P(a student does not like it) = 65/200

= 13/40

Ans: 13/40

Q8 (i) Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives less than 7 km from her place of work?

Answer:

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

Total no. of engineers = 40

Total no. of engineers who are living less than 7 km from their workplace = 9

Therefore we can say,

P(engineers who are living less than 7 km from their workplace)=

= 9/40

Ans: 9/40

Q8 (ii) Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives more than or equal to 7 km from her place of work?

Answer:

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

Total no. of engineers = 40

Total no. of engineers who are living less than 7 km from their workplace = 31

Therefore we can say,

P(engineers who are living more than or equal to 7 km from their workplace)=31/40

Ans: 31/40

Q8 (iii) Refer to Q.2, Exercise 14.2. What is the empirical probability that an engineer lives within 1/2 km from her place of work?

Answer:

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

Hey, don't you think its too simple:

Well, there is no such engineer whose distance between residence and place of work is less than 1/2 km

Therefore,

engineer whose distance between residence and place of work is less than 1/2 km =0

P(engineer whose distance between residence and place of work is less than 1/2 km) = 0

Ans: 0

Q9 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.

Answer:

This activity can be taken as a general problem:

Assumption:

Let the frequency of two-wheelers = x

Let the frequency of three-wheelers = y

Let the frequency of four-wheelers = z

Total no. of vehicles= x+y+z

therefore,

P(anyone vehicle out of the total vehicles I have observed is a two-wheeler) =

Q10 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.

Answer:

This activity can be taken as a general problem:

Well, we know the divisibility by 3 is when the sum of all the digits is divisible by 3

So,

The student will write the number between 100-999

There are 900 3 - digit numbers , which are 100, 101, 102, 103, ..., 999.

The first 3-digit numbers that are exactly divisible by 3 is 102, 105, ..... 999

total numbers which are divisible by 3 = 300

P(the sum of all the digits is divisible by 3) = 300/900

=1/3

Ans: 1/3

Q11 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.

Answer:

From the above question, the data of our interest is:

Total no. of bags = 11

Total no. of bags that contain more than 5 kg flour = 7

P(Bag contain more than 5 kg flour) = 7/11

Ans: 7/11

Q12 In Q.5, Exercise 14.2, you were asked to prepare a frequency distribution table, regarding the concentration of sulfur dioxide in the air in parts per million of a certain city for30 days. Using this table, find the probability of the concentration of sulfur dioxide in the interval 0.12 - 0.16 on any of these days.

Answer:

The data is representing the concentration of sulfur dioxide in the air in parts per million (ppm) of a city. The data obtained for a month of 30 days is as follows:

Total no. of days =30

No. of days in which Conc. of sulfur dioxide in the interval 0.12 - 0.16 = 2

P(Conc. of sulphur dioxide in the interval 0.12 - 0.16) =2/30

Ans: 1/15

Q13 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.

Answer:

The below-written data is representing the blood groups of 30 students study in class VIII.
A, B, O, O, B, A, O, O, AB, O, A, O, B, A, O
A, AB, O, A, A, B, A, B, O, O, O, AB, B, A, O

Total no. of students = 30

Total no. of students of this class who has blood group AB =3

P(Student of this class has blood group AB)= 3/30 => 1/10

Ans: 1/10