Class 10 - Probability Revision Notes Maths

Probability is a key concept in mathematics that helps us understand the chances of events occurring. In this guide, you’ll find concise and easy-to-understand notes covering fundamental ideas like experimental probability, theoretical probability, sample space, and key formulas.

Table of Contents

• What is Probability
• Key Terms in Probability
• Experimental (Empirical) Probability
• Theoretical (Classical) Probability
• Types of Events
• Solved Examples on Probability
• Common Mistakes to Avoid

What is Probability

Probability is the measure of how likely an event is to occur. It is expressed as a number between 0 and 1, where 0 means the event is absolutely impossible and 1 means it is completely certain. 

• P(E) =  Probability of the event

• Range of probability: 0 ≤ P(E) ≤ 1

Read more: Important Questions on Probability - Class 10

Key Terms in Probability

• Random experiment: A random experiment is an action or process whose outcome cannot be predicted with certainty, like rolling a die or drawing a card from a shuffled deck.

• Sample space: The set of all possible outcomes of an experiment is called the sample space.
  Example: Tossing a coin, S = {H, T}

• Outcome: An outcome is the single specific result of a trial.
  Example: Rolling a die and getting 4.

• Event (E): A collection of one or more outcomes is called an event.
  Example: Getting an even number on the dice.

• Favourable Outcome: Outcomes from the sample space that satisfy the condition of the event being considered are called 'favourable outcomes'.

Experimental (Empirical) Probability

Experimental probability (or empirical probability) is the likelihood of an event occurring based on actual, recorded data from experiments or trials rather than theoretical calculation. Experimental probability is never fixed. It changes slightly every time you repeat the experiment. As you increase the number of trials, the experimental probability slowly gets closer and closer to the theoretical probability.

Experimental (Empirical) P(E) = Number of times event E occurredTotal number of trials

Theoretical (Classical) Probability

Theoretical probability assumes that all outcomes are equally likely. Like a perfectly fair coin, an unbiased die, or a well-shuffled deck.

Theoretical probability P(E) =  Number of favourable outcomesTotal number of outcomes

Types of Events

 

Solved Examples on Probability

Example 1: A box contains 5 red marbles, 8 white marbles, and 4 green marbles. One marble is drawn at random. Find: (i) P(red), (ii) P(white), (iii) P(not green)
Solution: No. of red marbles = 5
No. of white marbles = 8
No. of green marbles = 4
Total number of marbles = 5 + 8 + 4 = 17.
(i) P(red) =  5/17 = 0.29

(ii) P(white) = 8/17 = 0.47

(iii) P(not green) = 1 - P(green) = 1 - (4/17) = 0.76

Example 2: A spinner has 8 equal sectors numbered 1 to 8. What is the probability of landing on: (i) number 8, (ii) a number > 2, (iii) an odd number?
Solution: Total outcome = 8
(i) P(number 8) = P (8) = 1/8
(ii) S = {3,4,5,6,7,8}  P(a number > 2) = 6/ 8 = 0.75
(iii) S = {1,3,5,7}, P(an odd number) = 4/8 = 0.5

 

Common  Mistakes to Avoid

•  Writing P(E) as a number greater than 1. Probability can NEVER exceed 1.

•  Forgetting to simplify fractions. 4/52 should be written as 1/13 in your final answer.

• In two-dice problems, writing total outcomes as 12 (6+6) instead of 36 (6×6). Outcomes multiply; they don't add.

• Confusing theoretical and experimental probability. Experimental probability changes with each set of trials; theoretical probability is fixed for a fair experiment.

• Counting Ace as a face card. In NCERT, face cards are only the Jack, Queen, and King. Ace is a separate card.