Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.4 Solutions The Mathematics of Maybe: Introduction to Probability

NCERT Solutions for Class 9 Maths Ganit Manjari Chapter 7 Exercise 7.4 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 and apply different concepts to solve problems based on possible outcomes and events.

The solutions explain each question in a simple and structured manner, making it easier for students to understand the concepts, check their answers and improve their problem-solving skills. A printable PDF is also available for quick revision and exam preparation.

Class 9 Maths Ganita Manjari Chapter 7 Exercise 7.4 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 7.4 Solutions The Mathematics of Maybe: Introduction to Probability

NCERT Solutions for Class 9 Maths Chapter 7 Exercise Set 7.4

Exercise Set 7.4 focuses on tree diagrams for multi-step experiments.

Question 1. 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.

Answer:
Basket A outcomes:

Apple, Orange, Orange

Basket B outcomes:

Banana, Mango

Tree structure:

Apple → Banana, Mango
Orange → Banana, Mango
Orange → Banana, Mango

Since the two oranges are identical in fruit type, the fruit-type pairs are:

Apple-Banana, Apple-Mango, Orange-Banana, Orange-Mango

Final answer:
The tree has branches from Basket A to Apple or Orange, and from each branch to Banana or Mango.

(ii) List the sample space.

Answer:
If only fruit types are recorded:

S = {(Apple, Banana), (Apple, Mango), (Orange, Banana), (Orange, Mango)}

If individual oranges are treated separately, there are 6 equally likely outcomes.

Final answer:
S = {(Apple, Banana), (Apple, Mango), (Orange, Banana), (Orange, Mango)}

(iii) What is the probability of picking one apple and one banana?

Answer:
Probability of apple from Basket A:

= 1/3

Probability of banana from Basket B:

= 1/2

So:

P(apple and banana) = 1/3 × 1/2
= 1/6

Final answer:
1/6

Question 2. A box contains 3 red pens, 4 black pens and 2 green pens. You pick a pen and put it back. Then your friend does the same.

(i) What are the possible outcomes of the pen colours? Draw a tree diagram.

Answer:
Possible colours:

Red, Black, Green

Since the pen is replaced, both picks have the same possible colour outcomes.

Sample space:

S = {(R, R), (R, B), (R, G), (B, R), (B, B), (B, G), (G, R), (G, B), (G, G)}

Tree structure:

Red → Red, Black, Green
Black → Red, Black, Green
Green → Red, Black, Green

Final answer:
S = {(R, R), (R, B), (R, G), (B, R), (B, B), (B, G), (G, R), (G, B), (G, G)}

(ii) Use the tree diagram to guess the probability that both you and your friend pick pens of the same colour.

Answer:
Total pens = 3 + 4 + 2 = 9

P(Red) = 3/9 = 1/3
P(Black) = 4/9
P(Green) = 2/9

Since the pen is replaced, the events are independent.

Probability of same colour:

= P(R, R) + P(B, B) + P(G, G)

= (3/9 × 3/9) + (4/9 × 4/9) + (2/9 × 2/9)

= 9/81 + 16/81 + 4/81
= 29/81

Final answer:
29/81

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