Probability in Maths

Last Updated : 17 Oct, 2026

Probability is a number between 0 and 1 that measures how likely an event is to happen. A probability of 0 means the event is impossible, 1 means it is certain, and values in between show how likely it is. For example, 0.5 means the event is as likely to happen as not.

The formula to calculate probability when all outcomes are equally likely is

\text{Probability} = \dfrac{Favourable \ Outcome}{Total \ Number \ of \ Outcomes}

  • Favorable outcomes refer to the outcome we are interested in.
  • Total outcomes represent the complete set of possible results an event can produce.

Below are a few examples illustrating the concept of probability in different situations:

Examples of Probability

What are the chances of the following events when we pick a random number from 1 to 10 ?

  • The number is divisible by 1
    100% are divisible by 1, as all numbers are completely divisible by 1, so we say probability is 1.
  • The number is divisible by 11
    0% are divisible by 11, as none of the numbers from 1 to 10 is divisible by it. All of them are smaller than 11, so the probability is 0.
  • The number is divisible by 2
    50% are divisible by 2, the favorable outcomes are 2, 4, 6, 8, 10, so we say probability is 1/2.
  • The number is divisible by 5
    20% are divisible by 5, the favorable outcomes are 5, 10, so we say probability is 1/5.

Why Learn Probability?

  1. Improves decision-making by helping us choose the best option when outcomes are uncertain.
  2. Probability is useful in real life, including weather forecasting, insurance, sports, medicine, and business.
  3. It develops logical thinking by improving reasoning and problem-solving skills.
  4. Probability is essential for data science and AI, as machine learning, artificial intelligence, and statistics rely heavily on it.

Probability for Beginners

Learn the basic ideas and applications of probability.

Problems that appear most often in exams and interviews.

For Aptitude Preparation

Practice probability questions commonly asked in exams.

Probability and Randomization

Explore advanced probability concepts and distributions.

Probability for Different Domains

See how probability is used in different fields.

For Programmers

Apply probability concepts in programming problems.

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