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Probability as favourable over total outcomes

For equally likely outcomes, probability of an event equals favourable outcomes divided by total outcomes.

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Student-friendly explanation

This is the working rule used in most Class 10 questions. The event may be getting an even number, a red ball, a heart card, or any other result we want. The key is to count only the outcomes that satisfy the event and divide by the full sample space.

How to write this in exams

  1. 1

    Start with the exact idea

    For equally likely outcomes, probability of an event equals favourable outcomes divided by total outcomes.

  2. 2

    Then show how to use it

    1. Identify the event. 2. List the favourable outcomes. 3. Count the total outcomes. 4. Divide favourable by total. 5. Simplify the fraction.

  3. 3

    Add one concrete example

    If a die is thrown, the probability of getting an even number is 3/6 = 1/2.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is 2/8 for the bag of balls because the student uses favourable outcomes over the remaining outcomes instead of the total.

Definition

For equally likely outcomes, probability of an event equals favourable outcomes divided by total outcomes.

Example

If a die is thrown, the probability of getting an even number is 3/6 = 1/2.

Rule to remember

P(E) = favourable outcomes / total outcomes, when the outcomes are equally likely.

Memory hook

Event count over total count.

Examples and method

Worked example

A bag has 2 white balls and 8 black balls. Probability of white = 2/10 = 1/5. The favourable outcomes are the white balls, and the total outcomes are all 10 balls.

Method to apply

1. Identify the event. 2. List the favourable outcomes. 3. Count the total outcomes. 4. Divide favourable by total. 5. Simplify the fraction.

Diagram support

A two-column table with favourable and total outcomes makes the counting very clear.

How CBSE asks it

Students are usually given a simple experiment and asked to find the probability of a named event.

Avoid common mistakes

Common confusion

Students sometimes count favourable outcomes correctly but forget to count the full sample space.

Common wrong answer

A common wrong answer is 2/8 for the bag of balls because the student uses favourable outcomes over the remaining outcomes instead of the total.

Exam tip

Write the event first, then count only matching outcomes before dividing by the total.

Quick check

A die is thrown once. Why is the probability of getting a prime number 3/6?

The favourable outcomes are 2, 3, and 5, so there are 3 favourable outcomes out of 6 total outcomes. That is why the probability is 3/6, which simplifies to 1/2.

Answer writing and exam use

1-mark answer

For equally likely outcomes, probability of an event equals favourable outcomes divided by total outcomes.

2-mark answer

For equally likely outcomes, probability of an event equals favourable outcomes divided by total outcomes. P(E) = favourable outcomes / total outcomes, when the outcomes are equally likely. If a die is thrown, the probability of getting an even number is 3/6 = 1/2.

3-mark answer

This is the working rule used in most Class 10 questions. The event may be getting an even number, a red ball, a heart card, or any other result we want. The key is to count only the outcomes that satisfy the event and divide by the full sample space. P(E) = favourable outcomes / total outcomes, when the outcomes are equally likely. A bag has 2 white balls and 8 black balls. Probability of white = 2/10 = 1/5. The favourable outcomes are the white balls, and the total outcomes are all 10 balls. Students are usually given a simple experiment and asked to find the probability of a named event. A common wrong answer is 2/8 for the bag of balls because the student uses favourable outcomes over the remaining outcomes instead of the total.
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