medium difficulty7 min

Probability as favourable over total outcomes

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

In one line: Event count over total count.

Understand it

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.

Example

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

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

A bag has 2 white balls and 8 black balls.

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

Method you can reuse

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

Visual tip

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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.

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.

Don't mix this up

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

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

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

1
Enough for 1 mark
For equally likely outcomes, probability of an event equals favourable outcomes divided by total outcomes.
2
Add for 2 marks
Example: If a die is thrown, the probability of getting an even number is 3/6 = 1/2.
3
Add for 3 marks
The event may be getting an even number, a red ball, a heart card, or any other result we want.

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