Question Bank — The Mathematics of Maybe: Introduction to Probability

NCERT Class 9 Mathematics · Chapter 7 · CBSE Board Pattern

Class 9 Mathematics Chapter 7 Question Bank CBSE Board Pattern

Section A — MCQs (10 questions, 1 mark each)

1. The probability of an impossible event is:
(a) 0 (b) 1 (c) 0.5 (d) between 0 and 1

2. Which of the following is an example of a random experiment?
(a) Tossing a fair coin (b) Measuring the length of a table (c) Adding 2 + 3 (d) Reading a fixed sentence

3. In the word “PROBABILITY”, the theoretical probability of picking the letter B is:
(a) 1/11 (b) 2/11 (c) 1/10 (d) 3/11

4. Experimental probability is calculated as:
(a) Number of favourable outcomes / Total possible outcomes
(b) Number of times the event occurred / Total number of trials
(c) Total trials / Favourable outcomes
(d) 1 – Theoretical probability

5. On the probability scale, an event with probability 0.5 is described as:
(a) Impossible (b) Less likely (c) Equally likely (d) Certain

6. The sample space for rolling a fair six-sided die is:
(a) {1, 2, 3, 4, 5} (b) {1, 2, 3, 4, 5, 6} (c) {Even, Odd} (d) {6}

7. If a coin is tossed twice, the number of elements in the sample space is:
(a) 2 (b) 3 (c) 4 (d) 6

8. The Law of Large Numbers states that as the number of trials increases, experimental probability:
(a) Moves away from theoretical probability (b) Tends to get closer to theoretical probability (c) Becomes zero (d) Becomes 1

9. Assertion (A): The probability of getting tails on a fair coin is always 1/2, even after six heads in a row.
Reason (R): Each toss of a fair coin is an independent event and the coin has no memory of previous outcomes.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

10. Assertion (A): When all outcomes are equally likely, theoretical probability = Number of favourable outcomes / Number of possible outcomes.
Reason (R): Theoretical probability is based on actual experimental data collected over many trials.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Section B — Very Short Answer (6 questions, 2 marks each)

1. Define a random experiment with one example from the chapter.
2. What is the difference between experimental probability and theoretical probability?
3. Write the sample space and its size when two fair coins are tossed simultaneously.
4. A fair die is rolled. What is the probability of getting a number greater than 4?
5. State the formula for experimental probability and give one situation where it is used.
6. What does a probability of 0 and a probability of 1 indicate on the probability scale?

Section C — Short Answer (5 questions, 3 marks each)

1. A bag contains 3 red, 2 blue and 1 green ball. One ball is drawn at random. Find the probability that the ball drawn is (i) red (ii) not red.
2. A letter is chosen at random from the word “GANITA”. Find the probability that the letter chosen is (i) a vowel (ii) not a vowel.
3. In a survey of 50 students, 20 like mangoes, 15 like apples, 10 like bananas and 5 like grapes. Find the experimental probability that a randomly chosen student likes (i) mangoes (ii) bananas.
4. A fair six-sided die is rolled 60 times and the number 3 appears 12 times. Find the experimental probability of rolling a 3. Also state the theoretical probability of rolling a 3.
5. List the sample space when a coin is tossed and a card is drawn from cards numbered 1 to 6. How many outcomes are there?

Section D — Long Answer (3 questions, 5 marks each)

1. A box contains 3 red pens, 4 black pens and 2 green pens. A pen is drawn at random, replaced, and then a second pen is drawn by a friend.
(i) Draw a tree diagram showing all possible outcomes.
(ii) List the sample space.
(iii) Find the probability that both pens are of the same colour.
(iv) Find the probability that the two pens are of different colours. (Multi-step problem)

2. Explain with examples why experimental probability may differ from theoretical probability. What happens to experimental probability when the number of trials becomes very large? Illustrate using the rolling of a fair die.

3. In a school of 1500 students, a sample of 50 students showed that 20 like Science Club, 15 like Arts Club, 10 like Sports Club and 5 like Debate Club.
(i) Find the experimental probability for each club from the sample.
(ii) Estimate how many students in the whole school are likely to prefer the Science Club.
(iii) Why might a larger and more representative sample give a better estimate?

Section E — Case/Source-Based (2 questions, 4 marks each)

Case 1: A teacher performs an experiment by tossing a fair coin 40 times. She records 22 heads and 18 tails.
(i) What is the experimental probability of getting heads?
(ii) What is the theoretical probability of getting heads?
(iii) Why is there a difference between the two probabilities?
(iv) If the teacher repeats the experiment 400 times, what do you expect to happen to the experimental probability?

Case 2: In a village fair, three snacks (Samosa, Pakora, Bhaji) and two drinks (Chai, Lassi) are available. A person chooses one snack and one drink at random.
(i) List the sample space of all possible combinations.
(ii) How many outcomes are there in the sample space?
(iii) Find the probability that a person chooses Samosa with any drink.
(iv) Find the probability that a person chooses Pakora and Lassi.

▶ Answer Key Attempt all questions first,
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Section A

  1. (a) — Impossible event has probability 0 (1 mark)
  2. (a) — Coin toss is unpredictable (1 mark)
  3. (b) — 2 favourable Bs out of 11 letters (1 mark)
  4. (b) — Formula from chapter (1 mark)
  5. (c) — Equally likely / even chance (1 mark)
  6. (b) — Standard sample space (1 mark)
  7. (c) — HH, HT, TH, TT (1 mark)
  8. (b) — Law of Large Numbers (1 mark)
  9. (a) — Both true; R explains independence (1 mark)
  10. (c) — A true; R false (theoretical needs no data) (1 mark)

Section B

  1. Random experiment: outcome cannot be predicted in advance though all possible outcomes are known. Example: tossing a coin. (1+1)
  2. Experimental uses actual trial data; theoretical assumes equally likely outcomes without data. (1+1)
  3. S = {HH, HT, TH, TT}, n(S) = 4 (1+1)
  4. Favourable = 2 (5,6), total = 6 → P = 2/6 = 1/3 (2 marks)
  5. Experimental P = (times event occurred)/(total trials). Used when collecting data from repeated trials. (1+1)
  6. 0 = impossible; 1 = certain (1+1)

Section C

  1. (i) 3/6 = 1/2 (1 mark formula + 1 mark substitution + 1 mark answer)
    (ii) 3/6 = 1/2
  2. (i) 3/6 = 1/2 (A, I, A) (1+1+1)
    (ii) 3/6 = 1/2
  3. (i) 20/50 = 0.4 (1+1+1)
    (ii) 10/50 = 0.2
  4. Experimental = 12/60 = 0.2; Theoretical = 1/6 (1.5+1.5)
  5. 2 × 6 = 12 outcomes (2 marks list, 1 mark count)

Section D

  1. (i) Tree diagram with first draw (3 branches) and second draw (3 branches each) (2 marks)
    (ii) 9 outcomes listed (1 mark)
    (iii) Same colour: (3/9 + 4/9 + 2/9) wait, correct pairs RR, BB, GG → 3+4+2 wait proper count gives 19/81? Wait: total 9 equally likely: RR, RB, RG, BR, BB, BG, GR, GB, GG. Same = RR,BB,GG = 3/9 = 1/3 (1 mark)
    (iv) Different = 6/9 = 2/3 (1 mark)
  2. Experimental varies with small trials; approaches theoretical with large trials (Law of Large Numbers). Example with die rolls given in text. (5 marks with points)
  3. (i) Science 20/50=0.4, etc. (2 marks)
    (ii) 0.4 × 1500 = 600 (2 marks)
    (iii) Larger sample reduces bias (1 mark)

Section E

Case 1

(i) 22/40 = 0.55 (1 mark)
(ii) 1/2 = 0.5 (1 mark)
(iii) Small number of trials (1 mark)
(iv) Experimental probability moves closer to 0.5 (1 mark)

Case 2

(i) 3 × 2 = 6 combinations listed (1 mark)
(ii) 6 (1 mark)
(iii) 2/6 = 1/3 (1 mark)
(iv) 1/6 (1 mark)

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All questions are answerable from the NCERT chapter text. Reviewed by GFIS faculty.