Class 9 Mathematics

Chapter 7 Solutions — The Mathematics of Maybe: Introduction to Probability

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Solutions

Overview

Step-by-step NCERT solutions for The Mathematics of Maybe: Introduction to Probability (Chapter 7, NCERT Class 9 Mathematics) — the full working for every question, not just the final answer. You can also read the The Mathematics of Maybe: Introduction to Probability textbook chapter.

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What these solutions cover

All 28 questions in The Mathematics of Maybe: Introduction to Probability are solved in the PDF. Here's what's inside, exercise by exercise:

The Probability Scale

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.
- (ii) It will snow in Mumbai in July.
- (iii) An elephant will walk through your classroom today.
- (iv) You will greet at least one friend…

Experimental Probability

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.
- (ii) If there are 600 sweets in total in the large bag, estimate how many are likely to be…
2.
A survey is conducted at a school where a random sample of 40 students is asked about their favourite club. The responses are: 14 students: Science Club | 11 students: Arts Club | 9 students: Sports Club | 6 students: Debate Club. Assume there are 800 students in the whole school.
- (i) What is the probability that a randomly chosen student from the sample prefers the Arts Club?
- (ii) Using the…
3.
Toss a coin 20 times and record the result each time (heads or tails).
- (i) How many times did you get heads?
- (ii) How many times did you get tails?
- (iii) Calculate the experimental probability of getting heads.
- (iv) If you toss the coin once more, what is the probability of getting tails?
Toss a paper cup into the air 100 times. After each toss record whether the cup lands on its bottom, upside down on its top, or on its side. Assign probabilities to the outcomes by using experimental probability.
What is the probability of getting an even number when rolling a fair 6-sided die?
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'?
- (ii) What is the theoretical probability of rolling a '3'?
- (iii) Why might these probabilities be different? What would you expect to happen if you roll the die 60, 600, or 6000 times?

Elements of Probability: Sample Spaces and Events

When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?
2.
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.
3.
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.'

Tree Diagrams

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.
- (ii) List the sample space.
- (iii) What is the probability of picking one apple and one banana?
2.
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…

Exercises

1.
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.
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).
3.
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.
4.
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…
A bag has 3 candies: strawberry, lemon, and mint. One is picked at random. What is the probability of picking a strawberry candy?
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.
7.
A tyre company records distances before replacement in 1000 cases. Distance (km): Less than 4000 -> 20 cases; 4001 to 9000 -> 210 cases; 9001 to 14000 -> 325 cases; More than 14000 -> 445 cases. 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.
8.
The letters of the word 'PEACE' are placed on cards (P, E, A, C, E). 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?
9.
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?
10.
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:
- (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?
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.
12.
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…
13.
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…
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.
15.
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}
Suppose you drop a dye at random on the rectangular region shown in Fig. 7.8 (a rectangle 3 m by 2 m). What is the probability that it will land inside the circle with a diameter of 1 m?

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