Probability – Class 10 Mathematics notes, important questions and MCQs

Chapter overview

Probability measures how likely an event is, from 0 (impossible) to 1 (sure), when all outcomes are equally likely.

Basics

• P(E) = number of favourable outcomes / total number of outcomes.
• 0 ≤ P(E) ≤ 1; P(sure event) = 1; P(impossible event) = 0.
• P(E) + P(not E) = 1.

Common experiments

• Coin: 2 outcomes. Two coins: 4 (HH, HT, TH, TT).
• Die: 6 outcomes. Two dice: 36 outcomes.
• Deck: 52 cards, 4 suits of 13; 12 face cards (J, Q, K); 26 red, 26 black.

Key terms

Event

a set of outcomes of an experiment

Complementary event

"not E", happens exactly when E does not

Elementary event

an event with only one outcome

Formulas

• P(E) = favourable / total
• P(not E) = 1 − P(E)

Important questions with answers

Quick revision

• P lies between 0 and 1.
• Sum of probabilities of all elementary events = 1.
• Two dice: 36 outcomes; sum 7 occurs 6 times.

Exam tips

• List the sample space for two coins or two dice before counting.
• Probability can never be negative or more than 1 — use this to reject options.

Practice MCQs

1. Probability of getting a head when a coin is tossed is

   1. 0
   2. 1/2
   3. 1
   4. 2
   Show answer

   Answer: (b) 1/2. 1 favourable out of 2.

2. Which cannot be a probability?

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

   Answer: (b) 1.5. Probability cannot exceed 1.

3. Probability of a sure event is

   1. 0
   2. 1
   3. 1/2
   4. −1
   Show answer

   Answer: (b) 1. It always happens.

4. A die is thrown once. P(prime number) =

   1. 1/6
   2. 1/3
   3. 2/3
   4. 1/2
   Show answer

   Answer: (d) 1/2. Primes 2, 3, 5: 3/6.

5. A card is drawn from a well-shuffled deck. P(red king) =

   1. 1/26
   2. 1/13
   3. 1/52
   4. 2/13
   Show answer

   Answer: (a) 1/26. 2 red kings / 52.

6. If P(E) = 0.05, then P(not E) =

   1. 0.05
   2. 0.5
   3. 0.95
   4. 0.9
   Show answer

   Answer: (c) 0.95. 1 − 0.05.

7. Two dice are thrown. P(sum = 8) =

   1. 5/36
   2. 1/6
   3. 1/9
   4. 7/36
   Show answer

   Answer: (a) 5/36. (2,6), (3,5), (4,4), (5,3), (6,2): 5/36.

8. A bag has 5 red and some blue balls. If P(blue) is twice P(red), the number of blue balls is

   1. 5
   2. 10
   3. 15
   4. 20
   Show answer

   Answer: (b) 10. x/(5 + x) = 2 × 5/(5 + x) ⇒ x = 10.