1. The theoretical probability of an event E is given by
(A) Number of trials in which E happened / Total number of trials
(B) Number of outcomes favourable to E / Number of all possible outcomes
(C) Number of all possible outcomes / Number of outcomes favourable to E
(D) 1 – Number of outcomes favourable to E
2. If P(E) = 0.37, then P(not E) equals
(A) 0.37 (B) 0.63 (C) 1 (D) 0
3. Which of the following cannot be the probability of an event?
(A) 2/3 (B) –1/2 (C) 0.7 (D) 15%
4. When a fair coin is tossed once, the probability of getting a tail is
(A) 0 (B) 1/2 (C) 1 (D) 2
5. An event that is sure to happen has probability
(A) 0 (B) 1/2 (C) 1 (D) greater than 1
6. Assertion (A): The probability of an impossible event is 0.
Reason (R): No outcome is favourable to an impossible event, so the numerator in the probability formula is zero.
(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.
7. Assertion (A): For any event E, P(E) + P(not E) = 1.
Reason (R): The events E and not E are complementary and together cover all possible outcomes of the experiment.
(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.
8. A bag contains 3 red and 5 black balls. One ball is drawn at random. The probability that the ball drawn is red is
(A) 3/8 (B) 5/8 (C) 3/5 (D) 1/2
9. When a fair die is thrown once, the probability of getting a number greater than 4 is
(A) 1/6 (B) 1/3 (C) 1/2 (D) 2/3
10. One card is drawn from a well-shuffled deck of 52 cards. The probability that the card is an ace is
(A) 1/13 (B) 1/52 (C) 4/13 (D) 1/4
11. State the definition of theoretical probability of an event E as given in the chapter.
12. If the probability of an event E is 0.25, find the probability of the complementary event.
13. A bag contains only lemon-flavoured candies. Malini draws one candy at random. What is the probability that she draws (i) a lemon-flavoured candy, (ii) an orange-flavoured candy?
14. Write the range of probability of any event E. Give one example each of an event whose probability is 0 and whose probability is 1.
15. In a group of 3 students, the probability that 2 students do not have the same birthday is 0.992. What is the probability that the two students have the same birthday?
16. Why is tossing a fair coin considered a fair way of deciding which team gets the ball at the start of a football match?
17. A box contains 3 blue, 2 white and 4 red marbles. One marble is drawn at random. Find the probability that the marble drawn is (i) white, (ii) blue, (iii) red.
18. A piggy bank contains hundred 50-paise coins, fifty ₹1 coins, twenty ₹2 coins and ten ₹5 coins. One coin falls out at random when the bank is turned upside down. Find the probability that the coin (i) is a 50-paise coin, (ii) is not a ₹5 coin.
19. A die is thrown once. Find the probability of getting (i) a prime number, (ii) a number lying between 2 and 6, (iii) an odd number.
20. One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting (i) a king of red colour, (ii) a face card, (iii) the jack of hearts.
21. A carton contains 100 shirts of which 88 are good, 8 have minor defects and 4 have major defects. One shirt is drawn at random. Find the probability that the shirt drawn (i) is acceptable to Jimmy (who accepts only good shirts), (ii) is acceptable to Sujatha (who rejects only shirts with major defects).
22. Two players Sangeeta and Reshma play a tennis match. It is known that the probability of Sangeeta winning is 0.62.
(i) What is the probability that Reshma wins the match?
(ii) What is the probability that Sangeeta does not win?
(iii) If the two events are complementary, verify that their probabilities add to 1. Give full justification using the chapter definition.
23. Harpreet tosses two different coins simultaneously.
(i) Write all possible outcomes.
(ii) Find the probability that she gets at least one head.
(iii) Find the probability that she gets no head.
(iv) Verify that the two probabilities add to 1 and identify the complementary events.
24. A box contains 90 discs numbered from 1 to 90. One disc is drawn at random. Find the probability that the disc bears (i) a two-digit number, (ii) a perfect square number, (iii) a number divisible by 5. Show all steps and use the theoretical probability formula.
25. In a school, Class X has 40 students of whom 25 are girls and 15 are boys. The class teacher puts identical name cards of all students in a bag and draws one card at random to select the class representative.
(i) What is the total number of possible outcomes?
(ii) Find the probability that the representative is a girl.
(iii) Find the probability that the representative is a boy.
(iv) Verify using the complement that the two probabilities obtained in (ii) and (iii) add to 1.
26. Savita and Hamida are friends. Ignoring leap years, assume each of the 365 days of the year is equally likely for a birthday.
(i) What is the total number of possible outcomes for Hamida’s birthday?
(ii) Find the probability that Hamida’s birthday is different from Savita’s birthday.
(iii) Find the probability that both have the same birthday.
(iv) Which event in (ii) and (iii) is the complement of the other? Verify the relation P(E) + P(not E) = 1.
1. (B) — correct formula as per NCERT definition (1 mark)
2. (B) 0.63 — P(not E) = 1 – P(E) (1 mark)
3. (B) –1/2 — probability cannot be negative (1 mark)
4. (B) 1/2 — equally likely outcomes, one favourable (1 mark)
5. (C) 1 — sure/certain event (1 mark)
6. (A) Both true and R explains A (1 mark)
7. (A) Both true and R explains A (1 mark)
8. (A) 3/8 — 3 favourable out of 8 (1 mark)
9. (B) 1/3 — 2 favourable (5,6) out of 6 (1 mark)
10. (A) 1/13 — 4 aces out of 52 (1 mark)
11. P(E) = Number of outcomes favourable to E / Number of all possible outcomes (assuming equally likely outcomes) — 2 marks
12. 0.75 — P(not E) = 1 – 0.25 (correct substitution and result) — 2 marks
13. (i) 1 (ii) 0 — only lemon candies present, impossible event has probability 0 — 2 marks
14. 0 ≤ P(E) ≤ 1; impossible event (0), sure event (1) — 2 marks
15. 0.008 — 1 – 0.992 (complementary events) — 2 marks
16. Coin is fair/unbiased; outcomes head and tail are equally likely — 2 marks
17. Total outcomes = 9
(i) P(W) = 2/9 (ii) P(B) = 3/9 = 1/3 (iii) P(R) = 4/9
(correct total — 1 mark; each probability — 1 mark) — 3 marks
18. Total coins = 180
(i) P(50p) = 100/180 = 5/9
(ii) P(not ₹5) = 170/180 = 17/18
(correct total — 1 mark; each probability — 1 mark) — 3 marks
19. Total outcomes = 6
(i) 3/6 = 1/2 (prime: 2,3,5) (ii) 3/6 = 1/2 (3,4,5) (iii) 3/6 = 1/2 (1,3,5)
(each correct fraction with reasoning — 1 mark) — 3 marks
20. (i) 2/52 = 1/26 (ii) 12/52 = 3/13 (iii) 1/52
(each correct with favourable count — 1 mark) — 3 marks
21. (i) 88/100 = 0.88 (ii) 96/100 = 0.96
(correct favourable counts and fractions — 3 marks)
22. (i) 0.38 (ii) 0.38 (iii) Complementary events; sum = 1 by NCERT relation — 5 marks (each part 1–2 marks with justification)
23. (i) (H,H), (H,T), (T,H), (T,T) (ii) 3/4 (iii) 1/4 (iv) Complementary; sum = 1 — 5 marks
24. Total = 90
(i) 81/90 (ii) 9/90 (iii) 18/90
(each with correct favourable count and simplification — 5 marks)
25. (i) 40 (ii) 25/40 = 5/8 (iii) 15/40 = 3/8 (iv) 5/8 + 3/8 = 1 — 4 marks (1 mark each sub-question)
26. (i) 365 (ii) 364/365 (iii) 1/365 (iv) Complementary; sum = 1 — 4 marks (1 mark each sub-question)
All questions are answerable from the NCERT chapter text. Reviewed by GFIS faculty.