Home NCERT SOLUTIONS 9th CLASS NCERT Class 9 Maths Chapter 15: Probability

NCERT Class 9 Maths Chapter 15: Probability

Ex 15.1 Class 9 Maths Question 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:
Here, the total number of trials = 30
∵ Number of times, the ball touched the boundary =6
∴ Number of times, the ball missed the boundary = 30 – 6 = 24

Ex 15.1 Class 9 Maths Question 2.
1500 families with 2 children were selected randomly, and the following data were recorded
NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 Q2
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:
Here, total number of families = 1500

(i) ∵ Number of families having 2 girls = 475
∴ Probability of selecting a family having 2 girls = [latex]\frac { 475 }{ 1500 } \quad =\quad \frac { 19 }{ 60 }[/latex]

(ii) ∵ Number of families having 1 girl = 814
∴ Probability of selecting a family having 1 girl = [latex]\frac { 814 }{ 1500 } \quad =\quad \frac { 407 }{ 750 }[/latex]

(iii) Number of families having no girl = 211
Probability of selecting a family having no girl = [latex]\frac { 211 }{ 1500 }[/latex]
Now, the sum of the obtained probabilities
[latex]\quad =\frac { 19 }{ 60 } +\frac { 407 }{ 750 } +\frac { 211 }{ 1500 } =\frac { 475+814+211 }{ 1500 } =\frac { 1500 }{ 1500 } =1[/latex]
i.e., Sum of the above probabilities is 1.

Ex 15.1 Class 9 Maths Question 3.
In a particular section of class IX, 40 students were asked about the month of their birth and the following graph was prepared for the data so obtained.
NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 Q3
Find the probability that a student of the class was born in August.
Solution:
From the graph, we have
Total number of students bom in various months = 40
Number of students bom in August = 6
∴ Probability of a student of the Class-IX who was bom in August [latex]\quad =\frac { 6 }{ 40 } +\frac { 3 }{ 20 }

Ex 15.1 Class 9 Maths Question 4.
Three coins are tossed simultaneously 200 times with the following frequencies of different outcomes.
NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 Q4
If the three coins are simultaneously tossed again, compute the probability of 2 heads coming up.
Solution:
Total number of times the three coins are tossed = 200
Number of outcomes in which 2 heads coming up = 72
∴ Probability of 2 heads coming up = [latex]\frac { 72 }{ 200 } \quad =\quad \frac { 9 }{ 25 }[/latex]
∴ Thus, the required probability = [latex]\frac { 9 }{ 25 }[/latex]

Ex 15.1 Class 9 Maths Question 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.
NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 Q5
Suppose a family is chosen. Find the probability that the family chosen is
(i) earning ₹ 10000-13000 per month and owning exactly 2 vehicles.

(ii) ∵ Number of families earning Rs. 16000 or more per month and owning exactly 1 vehicle = 579
∴ Probability of a family earning Rs. 16000 or more per month and owning exactly 1 vehicle = [latex]\frac { 579 }{ 2400 }[/latex]

(iii) ∵ Number of families earning less than Rs. 7000 per month and do not own any vehicle = 10
∴ Probability of a family earning less than Rs. 7000 per month and does not own any vehicle = [latex]\frac { 10 }{ 2400 }[/latex] = [latex]\frac { 1 }{ 240 }[/latex]

(iv) ∵ Number of families earning Rs. 13000 – Rs. 16000 per month and owning more than 2 vehicles = 25
∴ Probability of a family earning Rs. 13000 – Rs. 16000 per month and owning more than 2 vehicles = [latex]\frac { 25 }{ 2400 }[/latex] = [latex]\frac { 1 }{ 96 }[/latex]

(v) ∵ Number of families owning not more than 1 vehicle
= [Number of families having no vehicle] + [Number of families having only 1 vehicle]
= [10 + 1 + 2 + 1] + [160 + 305 + 535 + 469 + 579] = 14 + 2048 = 2062
∴ Probability of a family owning not more than 1 vehicle = [latex]\frac { 2062 }{ 2400 }[/latex] = [latex]\frac { 1031 }{ 1200 }[/latex]

Ex 15.1 Class 9 Maths Question 6.
A teacher wanted to analyse the performance of two sections of students in a mathematics test of 100 marks. Looking at their performances, 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
NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 Q6
(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) From the given table, number of students who obtained less than 20% marks = 7
Probability of a student obtaining less than 20% marks = [latex]\frac { 7 }{ 90 }[/latex]

(ii) From the given table, number of students who obtained marks 60 or above = [Number of students in class-interval 60 – 70] + [Number of students in the class interval 70 – above]
= 15 + 8 = 23
∴ Probability of a student who obtained 23 marks 60 or above = [latex]\frac { 23 }{ 90 }[/latex]

Ex 15.1 Class 9 Maths Question 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
NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 Q7
Find the probability that a student chosen at random
(i) likes statistics,
(ii) does not like it.
Solution:
Total number of students whose opinion is obtained = 200
(i) ∵ Number of students who like statistics = 135
∴ Probability of selecting a student who likes statistics = [latex]\frac { 135 }{ 200 }[/latex] = [latex]\frac { 27 }{ 40 }[/latex]

(ii) ∵ Number of students who do not like statistics = 65
∴ Probability of selecting a student who does not like statistics = [latex]\frac { 60 }{ 200 }[/latex] = [latex]\frac { 13 }{ 40 }[/latex]

Ex 15.1 Class 9 Maths Question 8.
The distance (in km) of 40 engineers from their residence to their place of work were found as follows
NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 Q8
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 [latex]\frac { 1 }{ 2 }[/latex] km from her place of work?
Solution:
Here, total number of engineers = 40

(i) ∵ Number of engineers who are living less than 7 km from their work place = 9
∴ Probability of an engineer who is living less than 7 km from her place of work = [latex]\frac { 9 }{ 40 }[/latex]

(ii) ∵ Number of engineers living at a distance more than or equal to 7 km from their work place = 31
∴ Probability of an engineer who is living at distance more than or equal to 7 km from her place of work = [latex]\frac { 31 }{ 40 }[/latex]

(iii) ∵ The number of engineers living within [latex]\frac { 1 }{ 2 }[/latex]km from their work place = 0
∴ Probability of an engineer who is living within [latex]\frac { 1 }{ 2 }[/latex]km from her place of work = [latex]\frac { 0 }{ 40 }[/latex] = 0

Ex 15.1 Class 9 Maths Question 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:
It is an activity. Students can do it themselves.

Ex 15.1 Class 9 Maths Question 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 digit is divisible by 3.
Solution:
A class room activity for students.

Ex 15.1 Class 9 Maths Question 11.
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.
Solution:
Here, total number of bags = 11
∵ Number of bags having more than 5 kg of flour = 7
∴ Probability of a bag having more than 5 kg of flour = [latex]\frac { 7 }{ 11 }[/latex]

Ex 15.1 Class 9 Maths Question 12.
A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city. The data obtained for 30 days is as follows
NCERT Solutions for Class 9 Maths Chapter 15 Probability Ex 15.1 Q12
You were asked to prepare a frequency distribution table, regarding the concentration of sulphur 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 sulphur dioxide in the interval 0.12-0.16 on any of these days.
Solution:
Here, total number of days = 30
∵ The number of days on which the sulphur dioxide concentration is in the interval 0.12 – 0.16 = 2
∴ Probability of a day on which sulphur dioxide is in the interval 0.12 – 0.16 = [latex]\frac { 2 }{ 30 }[/latex] = [latex]\frac { 1 }{ 15 }[/latex]

Ex 15.1 Class 9 Maths Question 13.
The blood groups of 30 students of class VIII are recorded as follows
A, B, 0, 0, AB, 0, A, 0, B, A, 0, B, A, 0, 0, A, AB, 0, A, A, 0, 0, AB, B, A, B, 0
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.
Solution:
Here, total number of students = 30
∵ Number of students having blood group AB = 3
∴ Probability of a student whose blood group is AB = [latex]\frac { 3 }{ 30 }[/latex] = [latex]\frac { 1 }{ 10 }

If you are searching for NCERT Solutions for Maths, you have reached the correct place. we have created most accurate and detailed solutions for Maths Problems Class wise and Chpter wise Exercises. All the Exercises updated as per new Revised syllabus

NCERT Class 9 Maths Solutions

Latest Posts

ఎడ్ సెట్ రిజల్ట్ చెక్ చేసుకొండి

టీఎస్ ఎడ్‌సెట్ ఫలితాలు విడుదల అయ్యాయి. ఉస్మానియా యూనివర్సిటీ ప్రాంగణంలో ఎడ్‌సెట్ ఫలితాలను ఉన్నత విద్యామండలి చైర్మన్ పాపిరెడ్డి విడుదల చేశారు. ఎడ్‌సెట్ ప్రవేశ పరీక్షలో 97.58 శాతం మంది...

రేపు ఎడ్​ సెట్​ రిజల్ట్స్​… వచ్చేనెల 6న లా సెట్‌, పీజీఎల్‌సెట్‌ ఫలితాలు

టీఎస్​ ఎడ్​సెట్​ రిజల్ట్స్​ ను రేపు రిలీజ్​ చేయనున్నట్లు ఎడ్​సెట్​ కన్వీన ర్ టి.మృణాళిని​ ప్రకటించారు. రెండేళ్ళ బీఈడీ కోర్సులో అడ్మిషన్లకు.. అక్టోబర్​ 1, 3 తేదీల్లో జరిగిన పరీక్షకు...

డెయిరీ టెక్నాలజీ కోర్సు కేరాఫ్ కామారెడ్డి

వ్యవసాయ అనుబంధ కోర్సుల్లో డెయిరీ టెక్నాలజీకి మంచి డిమాండ్ ఉంది. పీవీ నర్సింహారావు తెలంగాణ రాష్ట్ర పశువైద్య విశ్వవిద్యాలయం ఈ కోర్సును అందిస్తోంది. కోర్సు; డెయిరీ టెక్నాలజీకాల వ్యవధి;...

IIPH పబ్లిక్​ హెల్త్​లో పీజీ

డిగ్రీ పాసైన విద్యార్థులకు బెస్ట్ కోర్సు పబ్లిక్​ హెల్త్. హైదరాబాద్​ మాదాపూర్​లోని ఇండియన్ ఇన్​స్టిట్యూట్ ఆఫ్ పబ్లిక్ హెల్త్ లో 2020-21 ఏడాదికి మాస్టర్ డిగ్రీ కోర్సు అడ్మిషన్లకు నోటిఫికేషన్​...

ఒక్కసారి టెట్ పాసైతే.. లైఫ్ టైమ్​

టీచర్ ఎలిజిబిలిటీ టెస్టు (TET) విషయంలో నేషనల్ కౌన్సిల్ ఫర్ టీచర్ ఎడ్యుకేషన్ (NCTE) కీలక నిర్ణయం తీసుకుంది. టెట్ ఒకసారి అర్హత సాధిస్తే ఆ సర్టిఫికెట్ వాల్యూ జీవితకాలం...

MODEL PAPERS

PRACTICE PAPERS

EAMCET PREVIOUS PAPERS (TELANGANA)

2019-TS EAMCET TS EAMCET 2019 Engineering Question Paper with Key (3 May 2019...

NEET 2019 Question Papers with Solutions

NEET 2019 Question Papers with Solutions 05 May 2019

JEE 2020 January Papers With Solutions

JEE MATHS 2020 JANUARY 1 JEE Main 9-Jan-2020 Maths Paper Shift...

POLYCET Previous Question Papers with Key

TS POLYCET - 2020 Question Paper with Final Key (Held on 02.09.2020)

IBPS PO Previous Papers

IBPS PO 2019 PRELIMINARY Question Paper with SOLUTIONSIBPS PO 2018 PRELIMINARY Question Paper (13th OCTOBER 2018) with...

GATE 2020 Question Papers

GATE - 2020 Question Papers GATE 2020Question PapersQuestion PapersAE: Aerospace EngineeringIN: Instrumentation EngineeringAG:...

UGC NET Previous Papers

UGC NET Examination: Solved Paper 1: A few solved papers of UGC NET are included. The answer keys...

STUDY MATERIAL