DEMO
Look around freely · sample student, nothing is saved
Get the app
07
NCERT Solutions · Maths Ch 7
The Mathematics of Maybe: Introduction to Probability
27 questions · 5 exercises
Closed
Open all
Ex 7.1
Ex 7.2
Ex 7.3
Ex 7.4
Ex 7.5
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
1 QUESTIONS
Exercise 7.1
Q1
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 at school tomorrow.
(3 marks)
2
5 QUESTIONS
Exercise 7.2
Q1
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, 5 blue. (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 yellow, based on the sample results.
(3 marks)
Q2
A survey is conducted at a school where a random sample of 40 students is asked about their favourite club: 14 Science, 11 Arts, 9 Sports, 6 Debate. 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 sample results, estimate how many students in the whole school are likely to prefer the Sports Club.
(3 marks)
Q3
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?
(3 marks)
Q4
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.
(2 marks)
Q5
What is the probability of getting an even number when rolling a fair 6-sided die?
(1 mark)
3
3 QUESTIONS
Exercise 7.3
Q1
When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?
(1 mark)
Q2
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 marks)
Q3
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.’
(2 marks)
4
2 QUESTIONS
Exercise 7.4
Q1
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?
(3 marks)
Q2
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?
(3 marks)
5
EXERCISE 7.5 · 16 QUESTIONS
End-of-Chapter Exercises
Q1
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.
(2 marks)
Q2
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).
(1 mark)
Q3
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.
(3 marks)
Q4
Write the sample space and calculate the probability: (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?
(5 marks)
Q5
A bag has 3 candies: strawberry, lemon, and mint. One is picked at random. What is the probability of picking a strawberry candy?
(1 mark)
Q6
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.
(2 marks)
Q7
A tyre company records distances before replacement in 1000 cases: less than 4000 km: 20; 4001 to 9000 km: 210; 9001 to 14000 km: 325; more than 14000 km: 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.
(3 marks)
Q8
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?
(2 marks)
Q9
A game of chance consists of spinning an arrow 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?
(3 marks)
Q10
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?
(3 marks)
Q11
I throw a pair of 6-sided dice. Write down an event that has a probability of 0 and an event that has a probability of 1.
(2 marks)
Q12
Write the sample space and calculate the probability: (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?
(5 marks)
Q13
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?
(3 marks)
Q14
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.
(2 marks)
Q15
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}
(2 marks)
Q16
Suppose you drop a die 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?
Figure: a rectangle 3 m × 2 m with a circle of diameter 1 m inside it.
(2 marks)