NCERT Solutions Class 9 Maths Chapter 7 The Mathematics of Maybe: Introduction to Probability on Padhaiwise

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 7 The Mathematics of Maybe Exercise Set 7.1

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 7 — Exercise Set 7.1#

Probability is measured on a scale from 0 (impossible) to 1 (certain):

Label	Probability
Impossible	0
Less likely	between 0 and $\dfrac{1}{2}$
Equally likely (even chance)	$\dfrac{1}{2}$
More likely	between $\dfrac{1}{2}$ and 1
Certain	1

1. Rank the following events on a scale from 0 (Impossible) to 1 (Certain). Label each event: Impossible, less likely, equally likely (even chance), more likely, certain. Give reasons why you gave each event its ranking. #

(i) The next Monday will come after Sunday.

Certain — probability 1. Monday always follows Sunday; the order of the days of the week never changes.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 7 The Mathematics of Maybe Exercise Set 7.2

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 7 — Exercise Set 7.2#

$$\text{Experimental probability} = \dfrac{\text{Number of times the event occurred}}{\text{Total number of trials}}$$

$$\text{Theoretical probability} = \dfrac{\text{Number of favourable outcomes}}{\text{Number of possible outcomes}}$$

To estimate a total from a sample, multiply the sample probability by the size of the whole group.

1. A teacher mixes a large bag of sweets of different colours and randomly selects a sample of 30 sweets. She counts the number of sweets of each colour: 10 red sweets | 8 green sweets | 7 yellow sweets | 5 blue sweets #

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

$$P(\text{green}) = \dfrac{8}{30}$$

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 7 The Mathematics of Maybe Exercise Set 7.3

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 7 — Exercise Set 7.3#

The sample space $S$ lists every possible outcome exactly once; its number of elements $n(S)$ is the sample size. An event is a subset of the sample space.

1. When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space? #

Solution

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

∴ There are 6 possible outcomes: $n(S) = 6$.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 7 The Mathematics of Maybe Exercise Set 7.4

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 7 — Exercise Set 7.4#

A tree diagram lists all outcomes of a multi-step experiment: one branch for each outcome of the first step, then branches from each of those for the second step. Every path from start to end is one outcome.

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.

We label the oranges Orange 1 and Orange 2 so that all fruits in basket A are equally likely to be picked.

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 7 The Mathematics of Maybe End-of-Chapter Exercises

Mon, 01 Jan 0001 00:00:00 +0000

NCERT Solutions for Class 9 Maths Chapter 7 — End-of-Chapter Exercises#

$$P(E) = \dfrac{\text{Number of favourable outcomes}}{\text{Number of possible outcomes}}, \qquad 0 \leq P(E) \leq 1$$

$$P(\text{not } E) = 1 - P(E)$$
In a tree diagram, multiply the probabilities along a path, and add the probabilities of different paths.

1. Fill in the blanks. #

Answers

Statement	Blank
(i) The probability of an impossible event is ___.	0
(ii) The set of all possible outcomes of a random experiment is called the ___.	sample space
(iii) The probability of an event that is certain to happen is ___.	1
(iv) Tossing a fair coin has a probability of ___ for getting heads.	$\dfrac{1}{2}$

2. 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). #

Solution

The count 15 is the frequency. The fraction of all students is the relative frequency:

NCERT Solutions Class 9 Maths Chapter 7 The Mathematics of Maybe: Introduction to Probability on Padhaiwise

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 7 The Mathematics of Maybe Exercise Set 7.1

NCERT Solutions for Class 9 Maths Chapter 7 — Exercise Set 7.1#

1. Rank the following events on a scale from 0 (Impossible) to 1 (Certain). Label each event: Impossible, less likely, equally likely (even chance), more likely, certain. Give reasons why you gave each event its ranking. #

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 7 The Mathematics of Maybe Exercise Set 7.2

NCERT Solutions for Class 9 Maths Chapter 7 — Exercise Set 7.2#

1. A teacher mixes a large bag of sweets of different colours and randomly selects a sample of 30 sweets. She counts the number of sweets of each colour: 10 red sweets | 8 green sweets | 7 yellow sweets | 5 blue sweets #

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 7 The Mathematics of Maybe Exercise Set 7.3

NCERT Solutions for Class 9 Maths Chapter 7 — Exercise Set 7.3#

1. When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space? #

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 7 The Mathematics of Maybe Exercise Set 7.4

NCERT Solutions for Class 9 Maths Chapter 7 — Exercise Set 7.4#

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. #

NCERT Solutions for Class 9 Maths Ganita Manjari Chapter 7 The Mathematics of Maybe End-of-Chapter Exercises

NCERT Solutions for Class 9 Maths Chapter 7 — End-of-Chapter Exercises#

1. Fill in the blanks. #

2. 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). #

2. 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). #