Keerthana Classes

Maths ch14 probability

October 04, 2026

37 marks. Read the notes, then tap Start test. Answers and your score appear only after you submit.

Quick notes

Theoretical probability of an event E: P(E) = (number of outcomes favourable to E) ÷ (total number of possible outcomes), when all outcomes are equally likely.

0 ≤ P(E) ≤ 1. A sure event has probability 1; an impossible event has probability 0.

P(E) + P(not E) = 1. The probabilities of all elementary events of an experiment add up to 1.

A deck has 52 cards: 4 suits of 13; 26 red and 26 black; 12 face cards (J, Q, K); 4 aces.

Part A: Multiple choice 16 questions

1. The probability of a sure event is

  1. 0
  2. 1
  3. 1/2
  4. 2

It always happens.

2. The probability of an impossible event is

  1. 0
  2. 1
  3. −1
  4. 1/2

It never happens.

3. Which of these cannot be a probability?

  1. 0.7
  2. 2/3
  3. 0
  4. 1.5

Probability cannot exceed 1.

4. If P(E) = 0.05, then P(not E) is

  1. 0.05
  2. 0.5
  3. 0.95
  4. 1.05

1 − 0.05 = 0.95.

5. A coin is tossed once. P(head) is

  1. 1
  2. 1/2
  3. 0
  4. 1/4

2 equally likely outcomes, 1 favourable.

6. A die is thrown. P(a prime number) is

  1. 1/3
  2. 2/3
  3. 1/6
  4. 1/2

Primes 2, 3, 5: 3 out of 6.

7. A die is thrown. P(a number greater than 4) is

  1. 1/3
  2. 1/2
  3. 2/3
  4. 1/6

5 and 6: 2 out of 6.

8. A card is drawn from a deck of 52. P(a king) is

  1. 1/52
  2. 1/13
  3. 1/4
  4. 4/13

4 kings out of 52.

9. P(a red face card) from a deck of 52 is

  1. 3/13
  2. 6/13
  3. 3/26
  4. 1/26

6 red face cards out of 52.

10. A bag has 3 red and 5 black balls. P(red) is

  1. 3/5
  2. 5/8
  3. 1/3
  4. 3/8

3 out of 8.

11. Two coins are tossed. P(at least one head) is

  1. 3/4
  2. 1/2
  3. 1/4
  4. 1

HH, HT, TH: 3 out of 4.

12. Two dice are thrown. P(sum = 7) is

  1. 1/36
  2. 1/6
  3. 7/36
  4. 5/36

6 favourable outcomes out of 36.

13. Two dice are thrown. P(sum = 13) is

  1. 1/36
  2. 1/13
  3. 0
  4. 1

The largest possible sum is 12.

14. P(a leap year has 53 Sundays) is

  1. 1/7
  2. 53/366
  3. 1
  4. 2/7

The 2 extra days can be 7 pairs; 2 of them include Sunday.

15. A letter is chosen from MATHEMATICS. P(a vowel) is

  1. 4/11
  2. 3/11
  3. 5/11
  4. 7/11

A, E, A, I: 4 vowels out of 11 letters.

16. The sum of probabilities of all elementary events of an experiment is

  1. 0
  2. 1
  3. depends on the experiment
  4. 2

They cover every possible outcome.

Part B: Fill in the blanks 8 blanks

17. P(E) + P(not E) = [[1]].
18. The probability of an impossible event is [[0]].
19. A die is thrown. The probability of getting 6 is [[1/6]].
20. A bag has 5 red, 8 white and 4 green marbles. P(not green) = [[13/17]].
21. A card is drawn from a deck of 52. P(an ace) = [[1/13|4/52]].
22. Two coins are tossed. P(two heads) = [[1/4]].
23. A probability always lies between 0 and [[1]].
24. An event with only one outcome of the experiment is called an [[elementary]] event.

Part C: Questions and answers 9 questions

25. A box has 5 red, 8 white and 4 green marbles. One is taken out at random. Find P(red), P(white) and P(not green).

Total = 17.
P(red) = 5/17, P(white) = 8/17, P(not green) = 13/17.

26. Two dice are thrown together. Find the probability that the sum is 8.

Favourable: (2,6), (3,5), (4,4), (5,3), (6,2) = 5 out of 36.
P = 5/36.

27. A piggy bank has 100 coins of 50 p, 50 of ₹1, 20 of ₹2 and 10 of ₹5. One coin falls out. Find P(50 p coin) and P(not a ₹5 coin).

Total = 180.
P(50 p) = 100/180 = 5/9. P(not ₹5) = 170/180 = 17/18.

28. One card is drawn from a well-shuffled deck of 52. Find P(red king), P(face card), P(spade), P(queen of diamonds).

P(red king) = 2/52 = 1/26. P(face card) = 12/52 = 3/13.
P(spade) = 13/52 = 1/4. P(queen of diamonds) = 1/52.

29. A box has 90 discs numbered 1 to 90. Find P(two-digit number), P(perfect square), P(number divisible by 5).

Two-digit: 10 to 90 = 81, P = 9/10.
Squares 1, 4, …, 81 = 9, P = 1/10.
Multiples of 5: 18, P = 1/5.

30. 12 defective pens are mixed with 120 good ones. One pen is taken at random. Find the probability that it is good.

Total = 132. P(good) = 120/132 = 10/11.

31. Why is tossing a coin considered a fair way of deciding which team gets the ball first?

There are only two outcomes, head and tail, and they are equally likely. Each team has probability 1/2, so the result cannot be predicted or favoured.

32. A die is thrown once. Find P(an even prime number) and P(a number less than 6).

Even prime: only 2, so P = 1/6.
Less than 6: 1 to 5, so P = 5/6.

33. Two dice are thrown. Find the probability that the same number appears on both, and that different numbers appear.

Same: (1,1) … (6,6) = 6 out of 36, P = 1/6.
Different: 1 − 1/6 = 5/6.

Part D: Word puzzles 4 puzzles

Older lesson