NCERT Solutions for Class 9 Subjectwise

[Pages:21]NCERT Solutions for Class 9 Subjectwise

Class 9 Maths Class 9 Science Class 9 Science ? Chemistry Class 9 Science ? Biology Class 9 Science ? Physics Class 9 Social Science ? History Class 9 Social Science ? Geography Class 9 Social Science ? Civics Class 9 Social Science ? Economics Class 9 English

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#463422 Topic: Probability

List the outcomes you can see in these experiments. (a) Spinning a wheel (b) Tossing two coins together

Solution (a) Possible outcomes would be: A, B, C, D (b) Possible outcomes: HT, HH, TH, TT

#463423 Topic: Probability When a die is thrown, list the outcomes of an event of getting (i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than 5

Solution Possible outcomes: 1, 2, 3, 4, 5, 6 (i) (a) Prime numbers: 2, 3, 5 It represents the outcomes of Prime numbers (b) Not a prime number: 1, 4, 6 It represent the outcomes of not a prime numbers. (ii) (a) Number greater than 5: Only when 6 comes (b) Number not greater than 5: Only when outcomes: 1, 2, 3, 4 and 5

#463424 Topic: Probability

Find the (a) Probability of the pointer stopping on D in spinning a wheel if it has A, A, D, B, C written on it? (b) Probability of getting an ace from a well shuffled deck of 52 playing cards? (c) Probability of getting a red apple from the figure given above.

Solution

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(a) The pointer can stop at one of following regions A, A, B, C, D. Only in case that pointer will stop at region D. Probability: 1 5

(b) There are 52 cards: 4 ace cards Probability of getting an ace card 41 == 52 13

(c) There are a total of 7 apple, out of which 4 are red, 3 are green. Probability of red apple = 4 7

#463426 Topic: Probability Numbers 1 to 10 are written on ten separate slips (one number on one slip), kept in a box and mixed well. One slip is chosen from the box without looking into it. What is the probability of? (i) getting a number 6? (ii) getting a number less than 6? (iii) getting a number greater than 6? (iv) getting a 1-digit number?

Solution (i) Total slips: 10 Probability of getting a number 6 1

10

(ii) Numbers less than 6 : 1, 2, 3, 4, 5 51

Probability = 10 2

(iii) Number greater than 6 are 7, 8, 9, 10 42

Probability 6 = 10 5

(iv) Single digit: 1, 2, 3, 4, 5, 6, 7, 8, 9 Probability = 9

10

#463427 Topic: Probability If you have a spinning wheel with 3 green sectors, 1 blue sector and 1 red sector, what is the probability of getting a green sector? What is the probability of getting a non blue sector?

Solution Total sectors = 3 + 1 + 1 = 5

3 Probability of getting green sector =

5

Non-Blue sector: Green sector or Red sector Probability of getting non-blue = 4

5

#463428 Topic: Probability

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Find the probabilities of the events: When a die is thrown, list the outcomes of an event of getting (i) (a) a prime number (b) not a prime number. (ii) (a) a number greater than 5 (b) a number not greater than 5

Solution

(i) (a) Out of 6 possible outcomes, a prime number can be obtained in 3 cases. Probability of prime number = 3 = 1

62 (i) (b) Out of 6 possible outcomes, a prime number not obtained in 3 cases

31 Probability = =

62

(ii) (a)

Out of 6 possible outcomes, greater than 5 can be obtained 1 case Probability = 1

6 (ii) (b)

Out of 6 possible outcomes, a number not greater than 5 can be obtained in: 5 cases 5

Probability = 6

#464441 Topic: Probability 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 Number of times the batswoman hit a boundary = 6(given) Total balls she played = 30 Probability (hitting a boundary) = 6 = 1

30 5 Probability of not hitting a boundary = 1 - 1 = 4

55

#464443 Topic: Probability

No. of girls in a family 2

1

0

No. of families

475 814 211

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

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(i) Number of families having 2 girls = 475

Total families = 475 + 814 + 211 = 1500

P(2 girls) =

475

Total families

475 19

=

=

1500 60

814 407

(ii) P(1 girl) =

=

1500 750

211 (iii) P(No girl) =

1500

Sum of all these probabilities 19 407 211

=+ + 60 750 1500

475 + 814 + 211 =

1500

1500

=

=1

1500

Sum of these probabilities = 1

#464445 Topic: Probability

In a particular section of class IX, 40 students were asked about the month of their birth and following graph was prepared for data so obtained: Find the probability that a student of the class was born in August. Solution Number of students born in August = 6 Total number of students = 40 Probability of students born in August

Number of students born in August =

Total number of students 63 == 40 20

#464449 Topic: Probability

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Vehicles per family

0 1

2 Above 2

Monthly income (Rs.)

Less than 7,000

10 160 25 0

7,000 - 10,000

0 305 27 2

10,000 - 13,000

1 535 29 1

13,000 - 16,000

2 469 59 25

16,000 or more

1 579 82 88

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 - 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 - 16000 per month and owning more than 2 vehicles.

(v) owning not more than 1 vehicle.

Solution Number of families surveyed = 10 + 60 + 25 + 0 + 0 + 305 + 27 + 2 + 1 + 535 + = 2400

29 + 1 + 2 + 469 + 55 + 25 + 579 + 82 + 88

(i) Number of families earning Rs. 10000 - 13000 per month and owning exactly 2 vehicles = 29 29

P= 2400

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

P= 2400

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

10

1

P=

=

2400 240

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

25 1

P=

=

2400 96

(v) Number of families owning not more than 1 vehicle = 10 + 160 + 0 + 305 + 1 + 535 + 2 + 469 + 1 + 579 = 2062

2062 1031

P=

=

2400 1200

#464450 Topic: Probability

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Marks 0 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70 70 - Above Total

Number of Students 7 10 10 20 20 15 8 90

A teacher wanted to analyze the performance of two sections of students in a mathematics test of 100 marks. Looking at their performance, she found that a few students got,

under 20 marks and a few got 70 marks or above. So she decided to group them into intervals of varying sizes as follows: 0 - 20, 20 - 30.. . . , 60 - 70, 70 - 100 Then she

formed the following table.

(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 students = 90

(i) Number of students getting less than 20% marks in the test = 7 7

P= 90

(ii) Number of students obtaining marks 60 or above = 15 + 8 = 23 23

P= 90

#464460 Topic: Probability

Opinion like dislike

No. of students 135 65

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 students = 135 + 65 = 200

(i) Number of students liking stats = 135

135 27

P=

=

200 40

(ii) Number of students who dont like stats = 65

65 13

P=

=

200 40

#464461 Topic: Probability

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