Chapter 25 : Probability - Rd Sharma Solutions for Class 9 Maths CBSE

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Chapter 25 - Probability Excercise Ex. 25.1

Question 1
A coin is tossed 1000 times with the following frequencies:

Head : 455, Tail : 545

Compute the probability for each event.
Solution 1
Question 2

Two coins are tossed simultaneously 500 times with the following frequencies of different outcomes:

Two heads : 95 times

One tail : 290 times

No head : 115 times

Find the probability of occurrence of each of these events.

Solution 2

Question 3
Solution 3

Question 4
1500 families with 2 children were selected randomly and the following data were recorded:

Number of girls in a family: 0 1 2
Number of families: 211 814 475


If a family is chosen at random, compute the probability that it has:

(i) No girl

(ii) 1 girl

(iii) 2 girls

(iv) at most one girl

(v) more girls than boys
Solution 4

Question 5
In a cricket match, a batsman hits a boundary 6 times out of 30 balls he plays.

Find the probability that on a ball played:

(i) he hits boundary

(ii) he does not hit a boundary.
Solution 5

Question 6
The percentage of marks obtained by a student in monthly unit tests are given below:

Units Test: I II III IV V
Percentage of marks obtained: 69 71 73 68 76


Find the probability that the student gets:

(i) More than 70% marks

(ii) less than 70% marks

(iii) a distinction.
Solution 6

Question 7
Solution 7
Question 8
Solution 8
Question 9
Solution 9
Question 10

 

Following table shows the birth month of 40 students of class IX.

Jan

Feb

March

April

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

3

4

2

2

5

1

2

5

3

4

4

4

Find the probability that a student was born in August.

  

Solution 10

Question 11
Solution 11

Question 12

Solution 12
Question 13
Solution 13
Question 14
Solution 14

Chapter 25 - Probability Excercise 25.16

Question 1

The probability of an impossible event is

(a) 1

(b) 0

(c) less than 0

(d) greater than 1

Solution 1

The probability of an impossible event is always zero since the chances of occurring of that event is zero.

Hence, correct option is (b).

Question 2

The probability of a certain event is

(a) 0

(b) 1

(c) greater than 1

(d) less than 0

Solution 2

begin mathsize 12px style The space chances space of space occuring space of space an space certain space event space is space always space 100 percent sign.
Probability space equals space fraction numerator No. space of space Favorable space cases over denominator Total space No. space of space cases end fraction
Thus comma space for space straight a space certain space event comma
number space of space favorable space cases space equals space Total space number space of space cases
rightwards double arrow Probability space equals space 1
Hence comma space correct space option space is space left parenthesis straight b right parenthesis. end style

Question 3

The probability an event of a trial is

(a) 1

(b) 0

(c) less than 1

(d) more than 1

Solution 3

begin mathsize 12px style Probability space of space an space event space equals space fraction numerator No. space of space favorable space cases over denominator Total space No. space of space cases end fraction
Since space number space of space favourable space cases space can space not space be space greater space than space total space number space of space cases comma
probability space less than space 1
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

Question 4

begin mathsize 12px style Which space of space the space following space cannot space be space probability space of space an space event ?
left parenthesis straight a right parenthesis space 1 third
left parenthesis straight b right parenthesis space 3 over 5
left parenthesis straight c right parenthesis space 5 over 3
left parenthesis straight d right parenthesis space 1 end style

Solution 4

begin mathsize 12px style The space probability space of space an space event space always space lies space between space 0 space and space 1. space
Since space 5 over 3 space greater than space 1 comma space it space cannot space be space the space probability space of space an space event. space
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

Question 5

begin mathsize 12px style Two space coins space are space tossed space simultaneously. space The space probability space of space getting space atmost space one space head space is
left parenthesis straight a right parenthesis space 1 fourth
left parenthesis straight b right parenthesis space 3 over 4
left parenthesis straight c right parenthesis space 1 half
left parenthesis straight d right parenthesis space 1 fourth end style

Solution 5

begin mathsize 12px style If space two space coins space are space tossed space simultaneously comma space then space possible space cases space are space HH comma space TH comma space HT comma space TT
Total space number space of space cases space equals space 4
Number space of space favorable space cases space left parenthesis atmost space one space head right parenthesis equals space open parentheses HT comma space TH comma space TT close parentheses space equals space 3
Now comma space probability space of space getting space atmost space one space Head space equals 3 over 4
Hence comma space correct space option space is space left parenthesis straight b right parenthesis. end style

Chapter 25 - Probability Excercise 25.17

Question 1

A coin is tossed 1000 times, if the probability of getting a tail is 3/8, how many times head is obtained?

(a) 525

(b) 375

(c) 625

(d) 725

Solution 1

begin mathsize 12px style Probability space of space getting space straight a space tail space equals space 3 over 8
rightwards double arrow Probability space of space getting space straight a space head space equals space 1 minus 3 over 8 equals 5 over 8
Also comma space probability space of space getting space straight a space head space equals space fraction numerator No. space of space Heads space obtained over denominator Total space no. space of space trials end fraction
rightwards double arrow 5 over 8 space equals space fraction numerator No. space of space Heads space obtained over denominator 1000 end fraction
rightwards double arrow No. space of space Heads space obtained space equals space 5 over 8 cross times 1000 space equals space 625
Hence comma space correct space option space is space left parenthesis straight c right parenthesis. end style

Question 2

A dice is rolled 600 times and the occurrence of the outcomes 1, 2, 3, 4, 5 and 6 are given below:

Outcome 1 2 3 4 5 6
frequency 200 30 120 100 50 100

The probability of getting a prime number is

begin mathsize 12px style left parenthesis straight a right parenthesis space 1 third
left parenthesis straight b right parenthesis space 2 over 3
open parentheses straight c close parentheses space 49 over 60
open parentheses straight d close parentheses space 39 over 125 end style

Solution 2

begin mathsize 12px style Prime space numbers space in space 1 comma space 2 comma space 3 comma space 4 comma space 5 comma space 6 space are space colon space space 2 comma space 3 comma space 5
Number space of space times space 2 comma space 3 comma space 5 space occur space equals space 30 space plus space 120 space plus space 50 space equals space 200
Total space number space of space cases space equals space 200 space plus space 30 space plus space 120 space plus space 100 space plus space 50 space plus space 100 space equals 600 space
Required space Probability space equals fraction numerator Cases space when space we space obtained space left parenthesis 2 comma space 3 comma space 5 right parenthesis over denominator Total space No. space of space cases end fraction equals 200 over 600 equals 1 third
Hence comma space correct space option space is space left parenthesis straight a right parenthesis. end style

Question 3

The percentage of attendance of different classes in a year in a school is given below:

Class: X IX VIII VII VI V
Attendance: 30 62 85 92 76 55

What is the probability that the class attendance is more than 75%?

begin mathsize 12px style open parentheses straight a close parentheses space 1 over 6
open parentheses straight b close parentheses space 1 third
open parentheses straight c close parentheses space 5 over 6
open parentheses straight d close parentheses space 1 half end style

Solution 3

begin mathsize 12px style Total space number space of space classes space equals space 6
Number space of space classes space having space attendance space greater than space 75 percent sign space equals space VIII comma space VII comma space VI space equals space 3
rightwards double arrow Required space Probability space equals space 3 over 6 space equals space 1 half
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

Question 4

A bag contains 50 coins and each coin is marked from 51 to 100. One coin is picked at random. The probability that the number on the coin is not a prime number, is

begin mathsize 12px style open parentheses straight a close parentheses space 1 fifth
open parentheses straight b close parentheses space 3 over 5
open parentheses straight c close parentheses space 2 over 5
open parentheses straight d close parentheses space 4 over 5 end style

Solution 4

begin mathsize 12px style Prime space numbers space from space 51 space to space 100 colon
53 comma space 59 comma space 61 comma space 67 comma space 71 comma space 73 comma space 79 comma space 83 comma space 89 comma space 97
rightwards double arrow Number space of space prime space numbers space equals space 10
rightwards double arrow Number space of space non minus prime space numbers space equals space 50 space minus space 10 space equals space 40
Total space numbers space equals space 50
Thus comma space probability space of space getting space non minus prime space number space equals space 40 over 50 equals space 4 over 5
Hence comma space correct space option space is space left parenthesis straight d right parenthesis. end style

Question 5

In a football match, Ronaldo makes 4 goals from 10 penalty kicks. The probability of converting a penalty kick into a goal by Ronaldo, is

begin mathsize 12px style open parentheses straight a close parentheses space 1 fourth
open parentheses straight b close parentheses space 1 over 6
open parentheses straight c close parentheses space 1 third
open parentheses straight d close parentheses space 2 over 5 end style

Solution 5

begin mathsize 12px style Probability space that space Ronaldo space makes space straight a space goal space equals space fraction numerator Number space of space gools space made space in space all space kicks over denominator Total space number space of space Kics end fraction equals 4 over 10 equals 2 over 5
Hence comma space correct space optin space is space left parenthesis straight d right parenthesis. end style

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