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CraftExam
medium difficulty7 min

Probability of an event

Probability of an event is a number that shows how likely that event is to happen.

In one line: Favourable over total, not favourable over favourable.

Practice This Concept

Understand it

When all outcomes are equally likely, probability is found by dividing favourable outcomes by total outcomes. A bigger value means a greater chance of happening, while 0 means impossible and 1 means certain. In school problems, the sample space must be complete before you calculate probability.

Example

If a bag has 3 red balls and 2 blue balls, the probability of drawing a red ball is 3/5.

Formula and rule

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

Also, 0 ≤ P(E) ≤ 1.

See it worked out

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

Worked example

A box has 5 green and 7 yellow pens.

  1. 1One pen is chosen at random.
  2. 2Total outcomes = 12 pens.
  3. 3Favourable outcomes for green = 5.
  4. 4So P(green) = 5/12.

Method you can reuse

  1. 1Identify the experiment.
  2. 2Write the total number of equally likely outcomes.
  3. 3Count the favourable outcomes for the event.
  4. 4Substitute into P(E) = favourable/total.
  5. 5Simplify the fraction if needed.

Sketch it in your answer

Use a simple sample-space list or a tree diagram for coin and die experiments.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A fair coin is tossed once. What is the probability of getting a head?

Think first, then show answer
There are 2 equally likely outcomes, H and T, and only 1 favourable outcome, H. So the probability of getting a head is 1/2.

Common wrong answer

A common wrong answer is 5/7 for the box of pens because the student uses only the two colours and ignores the total number of pens.

Don't mix this up

Students sometimes divide by the number of favourable outcomes instead of the total number of outcomes.

Exam tip

First write the sample space or total number of outcomes, then count only the favourable ones.

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

Find the probability of a given event from a clear experiment, often with coins, dice, balls, or cards.
  1. 1

    Enough for 1 mark

    Probability of an event is a number that shows how likely that event is to happen.

  2. 2

    Add for 2 marks

    Example: If a bag has 3 red balls and 2 blue balls, the probability of drawing a red ball is 3/5.

  3. 3

    Add for 3 marks

    When all outcomes are equally likely, probability is found by dividing favourable outcomes by total outcomes.

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