Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.2 Solutions The Mathematics of Maybe: Introduction to Probability

NCERT Solutions for Class 9 Maths Ganit Manjari Chapter 7 Exercise 7.2 provide detailed, step-by-step solutions to the questions from The Mathematics of Maybe: Introduction to Probability. This exercise helps students strengthen their understanding of probability by exploring different outcomes and determining the likelihood of events.

The solutions explain each question in a simple and easy-to-follow manner, helping students improve their problem-solving skills and prepare effectively for exams. A printable PDF is also available for students to use for quick revision and practice.

Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.2 Solutions The Mathematics of Maybe: Introduction to Probability

The Mathematics of Maybe: Introduction to Probability
Medium
Q.
For the following experiments write down the sample space S.
(i) Rolling a die and tossing a coin together.
(ii) Choosing a random integer between – 5 and + 5.
(iii) A box containing 5 green and 7 red balls. One ball is drawn at random.
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
The letters of the word ‘PEACE’ are placed on cards. Leela draws a card without looking.
(i) What is the probability that it is a P, E or C?
(ii) What is the probability that it is not an E?
The Mathematics of Maybe: Introduction to Probability
Difficult
Q.
Three coins are tossed, and the number of heads is recorded. Which of the following lists is a sample space for this experiment? Why do the other lists fail to qualify as a sample space?
(i) {1, 2, 3}
(ii) {0, 1, 2}
(iii) {0, 1, 2, 3, 4}
(iv) {0, 1, 2, 3}
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
List the elements of a sample space for the simultaneous tossing of a coin and drawing of a card from a set of 6 cards numbered 1 through 6.
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
A box contains 4 balls numbered 1 to 4. Record a sample space using a tree diagram for the following experiments: 
(i) A ball is drawn, and the number is recorded. Then the ball is returned, and a second ball is drawn and recorded.
(ii) A ball is drawn and recorded. Without replacing the first ball, the experimenter draws and records a second ball.
(iii) What are the sizes of these two sample spaces?
The Mathematics of Maybe: Introduction to Probability
Difficult
Q.
Write the sample space and calculate the probability based on the given information.
(i) Two dice are rolled. What is the probability that the sum is a prime number greater than 5?
(ii) A bag contains 4 red, 3 green, and 2 blue balls. Two balls are drawn without replacement. What is the probability that both are of different colours?
(iii) Three coins are tossed. What is the probability that the first coin shows heads and exactly two heads occur in total?
(iv) A four-digit number is formed using the digits 1, 2, 3, and 4 with no repetition. What is the probability that the number is even?
(v) A student takes a multiple-choice test with 3 questions, each having 4 options (A, B, C, D), with only one correct answer. What is the probability that the student guesses and gets exactly 2 answers correct?
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
I throw a pair of 6-sided dice. Write down an event that has a probability of 0 and an outcome that has a probability of 1.
The Mathematics of Maybe: Introduction to Probability
Difficult
Q.
A basket contains 4 red balls and 5 blue balls. One ball is drawn and laid aside, and a second ball is drawn. Draw a tree diagram to represent the possible outcomes and probabilities. Use the tree diagram to answer the following questions.
(i) What is the probability of drawing a red ball and then a blue ball?
(ii) What is the probability of drawing 2 blue balls?
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
A game of chance consists of spinning an arrow (see Fig. 7.7.) which comes to rest pointing at one of the numbers 1, 2, 3, 4, 5, 6, 7, 8, and these are equally likely outcomes. What is the probability that it will point at
(i) 8?
(ii) An odd number?
(iii) A number greater than 2?
(iv) A number less than 9?
(v) A multiple of 3?
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
A tyre company records distances before replacement in 1000 cases.
Distance
(km)
Less than
4000
4001 to
9000
9001 to
14000
More than
14000
Number of
cases
20
210
325
445
Find the probability that a randomly chosen tyre lasts:
(i) Less than 4000 km.
(ii) Between 4000 and 14000 km.
(iii) More than 14000 km.
The Mathematics of Maybe: Introduction to Probability
Easy
Q.
In a village fair, there are 3 popular snacks available: Samosa, Pakora, and Bhaji. For drinks, villagers can choose either Chai or Lassi.
(i) List the sample space of all possible snack and drink combinations a person could choose at the fair.
(ii) List the event ‘Selecting Samosa as a snack.’
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
A child has 2 shirts (one red and one blue) and 3 types of pants (jeans, khakis, and shorts). List all the possible combinations of outfits consisting of one shirt and one pair of pants. Display your answer in a table format.
The Mathematics of Maybe: Introduction to Probability
Easy
Q.
A bag has 3 candies: strawberry, lemon, and mint. One is picked at random. What is the probability of picking a strawberry candy?
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
Write the sample space and calculate the probability based on the given information.
(i) Two coins are tossed at the same time. What is the probability of getting at least one head?
(ii) Ten identical cards numbered 1 to 10 are placed in a box. One card is drawn at random. What is the probability of drawing a card with an even number?
(iii) A die is rolled once. What is the probability of getting a number greater than 4?
(iv) A bag contains 3 red balls, 2 blue balls, and 1 green ball. One ball is picked at random. What is the probability that it is not red?
(v) Three coins are tossed simultaneously. What is the probability of getting exactly two heads?
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
Which of the following experiments have equally likely outcomes? Explain.
(i) A driver attempts to start a car. The car starts or does not start.
(ii) Tossing a fair coin once.
(iii) Rolling a fair 6-sided die.
(iv) Choosing a marble randomly from a bag that contains 3 red marbles and 7 blue marbles.
(v) A baby is born. It is a boy or a girl.
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
In a survey of 50 students, 15 students said they liked football. The number of students who like football is 15, and the ________ (frequency/relative frequency) is __________ (fill in the fraction or decimal).
The Mathematics of Maybe: Introduction to Probability
Easy
Q.
Fill in the blanks.
(i) The probability of an impossible event is _______.
(ii) The set of all possible outcomes of a random experiment is called the __________.
(iii) The probability of an event that is certain to happen is _______.
(iv) Tossing a fair coin has a probability of ______ for getting heads.
The Mathematics of Maybe: Introduction to Probability
Difficult
Q.
Let us say that you have a box containing 3 red pens, 4 black pens and 2 green pens. You pick a pen (without looking) from the box and put it back. Then your friend does the same.
(i) What are the possible outcomes of the pen colours? Can you draw a tree diagram representing the possible outcomes?
(ii) Can you use the tree diagram to guess the probability that both you and your friend pick pens of the same colour?
The Mathematics of Maybe: Introduction to Probability
Medium
Q.
There are two fruit baskets A and B. Basket A has one apple and two oranges. Basket B has one banana and one mango. You randomly pick one fruit from each basket.
(i) Draw a tree diagram showing all possible pairs of fruits.
(ii) List the sample space.
(iii) What is the probability of picking one apple and one banana?
The Mathematics of Maybe: Introduction to Probability
Difficult
Q.
Suppose you drop a dye at random on the rectangular region shown in Fig. 7.8. What is the probability that it will land inside the circle with a diameter of 1 m?

Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.2 Solutions The Mathematics of Maybe: Introduction to Probability

NCERT Solutions for Class 9 Maths Chapter 7 Exercise Set 7.2

Exercise Set 7.2 focuses on experimental probability, theoretical probability, data-based estimation and relative frequency.

Question 1. A teacher mixes a large bag of sweets of different colours and randomly selects a sample of 30 sweets: 10 red, 8 green, 7 yellow and 5 blue.

(i) Calculate the probability that a randomly picked sweet from the sample is green.

Answer:
Number of green sweets = 8
Total sweets in sample = 30

Experimental probability of green sweet:

= 8/30
= 4/15

Final answer:
4/15

(ii) If there are 600 sweets in total in the large bag, estimate how many are likely to be yellow.

Answer:
Number of yellow sweets in sample = 7
Total sweets in sample = 30

Experimental probability of yellow sweet:

= 7/30

Estimated number of yellow sweets in 600:

= 7/30 × 600
= 7 × 20
= 140

Final answer:
About 140 yellow sweets

Question 2. A random sample of 40 students is asked about their favourite club: 14 Science Club, 11 Arts Club, 9 Sports Club and 6 Debate Club. Assume there are 800 students in the school.

(i) What is the probability that a randomly chosen student from the sample prefers the Arts Club?

Answer:
Number of students preferring Arts Club = 11
Total students in sample = 40

Probability:

= 11/40
= 0.275

Final answer:
11/40 or 0.275

(ii) Estimate how many students in the whole school are likely to prefer the Sports Club.

Answer:
Number of students preferring Sports Club = 9
Total sample = 40

Probability of Sports Club preference:

= 9/40

Estimated number in 800 students:

= 9/40 × 800
= 9 × 20
= 180

Final answer:
About 180 students

Question 3. Toss a coin 20 times and record the result each time.

(i) How many times did you get heads?

Answer:
This answer depends on the actual experiment.

Final answer:
Record the number of heads from your 20 tosses.

(ii) How many times did you get tails?

Answer:
This answer depends on the actual experiment.

If heads = H, then:

Tails = 20 - H

Final answer:
Tails = 20 - number of heads

(iii) Calculate the experimental probability of getting heads.

Answer:
Experimental probability:

= Number of heads / Total tosses
= H/20

Final answer:
Experimental probability of heads = H/20

(iv) If you toss the coin once more, what is the probability of getting tails?

Answer:
For a fair coin, each toss is independent.

The theoretical probability of tails is:

= 1/2

Final answer:
1/2

Question 4. Toss a paper cup into the air 100 times. Record whether the cup lands on its bottom, upside down on its top or on its side. Assign probabilities using experimental probability.

Illustration of a child tossing a red paper cup onto a table, showing three possible landing positions: upright on the bottom, upside down on the top, and lying on the side.

Answer:
Let:

Number of times cup lands on bottom = B
Number of times cup lands on top = T
Number of times cup lands on side = S

Total trials = 100

Experimental probabilities:

P(bottom) = B/100
P(top) = T/100
P(side) = S/100

Final answer:
Use the recorded frequencies: B/100, T/100 and S/100.

Question 5. What is the probability of getting an even number when rolling a fair 6-sided die?

Answer:
Sample space:

S = {1, 2, 3, 4, 5, 6}

Even outcomes:

{2, 4, 6}

Number of favourable outcomes = 3
Total outcomes = 6

Probability:

= 3/6
= 1/2

Final answer:
1/2

Question 6. Suppose you roll a 6-sided die 12 times and get a 3 three times.

(i) What is the experimental probability of rolling a 3?

Answer:
Number of times 3 occurred = 3
Total rolls = 12

Experimental probability:

= 3/12
= 1/4

Final answer:
1/4

(ii) What is the theoretical probability of rolling a 3?

Answer:
A fair die has 6 equally likely outcomes.

Only one outcome is 3.

Theoretical probability:

= 1/6

Final answer:
1/6

(iii) Why might these probabilities be different? What would happen if you roll the die 60, 600 or 6000 times?

Answer:
Experimental probability is based on actual results. Theoretical probability is based on equally likely outcomes.

With only 12 rolls, experimental results may differ from theoretical probability.

As the number of rolls increases, the experimental probability is expected to get closer to 1/6.

Final answer:
They differ because of random variation. With more trials, experimental probability usually gets closer to theoretical probability.

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