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Question 5

The number of hours for which students of a particular class watched television during holidays is shown through the given graph.

Answer the following.

(i) For how many hours did the maximum number of students watch TV?

(ii) How many students watched TV for less than 4 hours?

(iii) How many students spent more than 5 hours in watching TV?

Solution:
(i) 4 - 5 hours

(ii) 34 students

(iii) 14 students

Question 6

A survey was made to find the type of music that a certain group of young people liked in a city. Adjoining pie chart shows the findings of this survey. From this pie chart answer the following:

(i) If 20 people liked classical music, how many young people were surveyed?

(ii) Which type of music is liked by the maximum number of people?

(iii) If a cassette company were to make 1000 CD’s, how many of each type would they make?

Solution:
(i) 200 people

(ii) Light music

(iii) A cassette company would make 100 CD's of Classical music, 200 CD's of Semi classical music, 400 CD's of Light music and 300 CD's of Folk music

Question 7

A group of 360 people were asked to vote for their favourite season from the three seasons rainy, winter and summer.

(i) Which season got the most votes?

(ii) Find the central angle of each sector.

(iii) Draw a pie chart to show this information.

Season

No. of Votes

Summer

90

Rainy

120

Winter

150


Solution:
(i) Winter season

(ii) The central angle of the Winter season sector is 150°, Rainy season sector is 120° and Summer season sector is 90°

(iii)Total number of votes = 360 the corresponding angles of summer,rainy and winter seasons are 90° , 120° and 150° respectively


Question 8

Draw a pie chart showing the following information. The table shows the colors preferred by a group of people.

 

Colors

No. of People

Blue

18

Green

9

Red

6

Yellow

3


Solution:
Total number of people in a group = 36

Therefore corresponding central angles are calculated as below:
 

Colours

No. of People

In Fractions

Central Angle

Blue

18

Green

9

Red

6

Yellow

3




Question 9

The adjoining pie chart gives the marks scored in an examination by a student in Hindi, English, Mathematics, Social Science and Science. If the total marks obtained by the students were 540, answer the following questions.

(i) In which subject did the student score 105 marks?

(Hint: for 540 marks, the central angle = 360°.

So, for 105 marks, what is the central angle?)

(ii) How many more marks were obtained by the student in Mathematics than in Hindi?

(iii) Examine whether the sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi.

(Hint: Just study the central angles).


Solution:
Total marks scored = 540

(i) Mark scored in the subject = 105

       The central angle for 105 marks =

       From the pie chart we see that the central angle for Hindi is 70° .

        ∴The student has scored 105 marks in Hindi.

(ii) The central angle for Mathematics = 90°

         ∴The marks obtained by the student in Mathematics =

          ∴The difference in the marks obtained in Mathematics and Hindi = 135 - 105 = 30

          ∴The student has scored 30 marks more in Mathematics than in Hindi.

(iii) Sum of the central angles for Social Science and Mathematics = 90° + 65° = 155°

         Sum of the central angles for Science and Hindi = 80° + 70° = 150°

          ∴The sum of the marks obtained in Social Science and Mathematics is more than that in Science and Hindi

Question 10

The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart.

 

Language

Hindi

English

Marathi

Tamil

Bengali

Total

Number of Students

40

12

9

7

4

72


Solution:
Total number of students in a hostel = 72

The central angle for drawing the pie chart is calculated as follows:

Language

Number of Students

In Fractions

Central Angle

Hindi

40

English

12

Marathi

9

Tamil

7

Bengali

4

Question 11

List the outcomes you can see in these experiments.

(a) Spinning a wheel

(b) Tossing two coins together


Solution:
(a) The outcomes of the spinning wheel are A, B, C, D

(b) The outcomes of tossing two coins together are HT, HH, TH, TT.

Question 12

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) The outcomes of getting a prime number are 2, 3, 5
(b) The outcomes of getting not a prime number are 1, 4, 6

(ii)
(a) The outcomes of getting a number greater than 5 is 6
(b) The outcomes of getting a number not greater than 5 are 1, 2, 3, 4, ,5


Question 13


Find the

(a) Probability of the pointer stopping on D in the spinner given below.

(b) Probability of getting an ace from a well shuffled deck of 52 playing cards.

(c) Probability of getting a red apple from the basket shown below.

Solution:
(a) Total number of outcomes = 5
           Getting a D consists of 1 outcome.
          
Probability of getting a D =

(b) Total number of outcomes = 52
          Getting an ace consists of 4 outcome.
          ∴Probability of getting an ace =

(c) Total number of outcomes = 7
          Getting a red apple consists of 4 outcome.
          ∴Probability of getting a red apple =


Question 14

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 number of outcomes = 10
               The number of outcomes for getting the number 6 = 1  
               \ Probability of getting the number 6 =

(ii) The number of outcomes for getting a number less than 6 = 5

             ∴Probability of getting a number less than 6 =

(iii) The number of outcomes for getting a number greater than 6 = 4
            ∴Probability of getting a number greater than 6 =

(iv) The number of outcomes for getting a 1-digit number = 9
            ∴Probability of getting a 1-digit number =

 

Question 15

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 number of outcomes = 3 + 1 + 1 = 5
The number of outcomes for getting a green sector = 3
∴Probability of getting a green sector =
The number of outcomes for getting a non blue sector = 4
∴Probability of getting a non blue sector =


Question 16

When a die is thrown, find the probability 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:
Total number of outcomes = 6

(i) (a) The number of outcomes for getting a prime number = 3
             ∴Probability of getting a prime number =

(b) The number of outcomes for getting not a prime number = 3
            ∴Probability of getting not a prime number =

(ii) (a) The number of outcomes for getting a number greater than 5 = 1
           ∴ Probability of getting a number greater than 5 =

(b) The number of outcomes for getting a number not greater than 5 = 5
           ∴Probability of getting a number not greater than 5 =





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