Students often struggle with probability questions in Class 10 CBSE Maths. One small counting error changes the final answer. Many students know the formula but fail to apply it correctly during exams.

The probability chapter focuses on theoretical probability and equally likely outcomes. CBSE questions use fixed patterns based on coins, dice, playing cards, and number selection. Each problem tests how well students identify the sample space, count favourable outcomes, and apply the standard probability formula.

This blog explains all Class 10 probability formulas with clear logic, solved examples, and exam-focused explanations. It helps students avoid common mistakes and score consistently in board exams.

Probability Formula and Symbols

Probability measures the likelihood of an event in a random experiment. CBSE uses one core formula for all probability questions.

Standard Probability Formula: P(A) = n(A) ÷ n(S)

Where:

A favourable outcome means the outcome of interest, not a successful or positive result.

Complete List of Probability Formulas

The table below includes all formulas required for CBSE board exams, including conditions and correct interpretation.

Core Probability Rules

Fundamental Properties

Key Probability Terms for Exams

• Experiment: An action with an uncertain outcome
• Sample Space: All possible outcomes of an experiment
• Event: A group of outcomes from the sample space
• Favourable Outcomes: Outcomes that satisfy the event
• Trial: One performance of an experiment
• Certain Event: Probability equals 1
• Impossible Event: Probability equals 0

Applications of Probability Formula Class 10

Probability helps us predict how likely an event is to occur when the outcome is uncertain. It is widely used in daily life and decision making.

• Used in weather prediction to estimate chances of rain or temperature change
• Applied in games and sports to study winning possibilities
• Helps insurance companies calculate risk and premiums
• Used in traffic planning to predict congestion patterns
• Applied in medical studies to measure treatment success rates

Tips to Memorize Probability Formula Class 10

• Start with Concepts: Focus on understanding what probability represents and how each formula works rather than just memorizing numbers.
• Visualize Problems: Draw diagrams, tables, or use coins/dice/cards to see outcomes. This makes abstract problems easier to grasp.
• Practice Regularly: Solve a variety of questions from your textbook and additional reference books to cover all types of scenarios.
• Check Units and Fractions: Always simplify probabilities to fractions or decimals and double-check the total outcomes.
• Understand Complementary Events: Remember P(not A) = 1 − P(A) — often used in trick questions.
• Learn from Mistakes: Review incorrect answers from practice sessions to avoid repeating them in exams.

Probability Solved Examples

Example 1: Drawing a Card

A card is drawn at random from a standard deck of 52 playing cards. Find the probability of drawing:

• A red card
• A king

Solution

• Total cards = 52
• Number of red cards = 26
• Probability of red card = 26/52 = 1/2
• Number of kings = 4
• Probability of king = 4/52 = 1/13

Example 2: Throwing a Die

A die is thrown once. Find the probability of getting:

• A number greater than 4
• An even number

Solution

Sample space = {1, 2, 3, 4, 5, 6}

• Numbers greater than 4 = {5, 6}
  Probability = 2/6 = ⅓
• Even numbers = {2, 4, 6}
  Probability = 3/6 = 1/2

Example 3: Selecting a Student

A class has 20 students:

• 12 boys
• 8 girls

One student is chosen at random. Find the probability that the selected student is:

• A boy
• A girl

Solution

• Probability of selecting a boy = 12/20 = 3/5
• Probability of selecting a girl = 8/20 = 2/5