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# Introduction to Probability

As an introduction to probability, we can say that probability is a measure of the likelihood of a particular event occuring or happening.

Sometimes we describe various situations in our day to day lives in probability terms, such as “getting struck by lightning is almost impossible”, or “there is a very good chance of rain tomorrow”, or “the probability of having twins is 1 in 500”, and so on.

Some of the words used to express probability of something happening is impossible, even chance, unlikely, likely, certain, 50-50, and so on. When we use such words to describe the likelihood of something happening (an event), we call it the “chance of an event”.

We also (sometimes) describe the likelihood of something happening in numbers (such as 1 in 10 times, or 50-50, etc.).

Typically, probability is measured on a scale between 0 and 1. It can also be expressed in fractions, decimals or percentage form.

• If an event is impossible to occur, then the probability of that event is zero.
• If an event is sure/certain to happen, then the probability of that event  is one.
• If an event has a 50-50, or an even chance of occuring, then the probability of that event is 0.5.
• An event that is unlikely to occur will have a probability between 0 and 0.5, while an event that is likely to occur will have a probability between 0.5 and 1.

The likelihoods of events and their probabilities are shown below pictorially:

Examples:

1. Scoring 120% in an examination is impossible.
2. Tossing a coin and getting heads is an even chance.
3. The sun will rise in the east is a certain event.
4. Rolling a dice and getting a ‘2’ on the top face is unlikely.
5. A bag has 12 red balls, 5 green balls and 3 blue balls. Choosing a green ball is unlikely, but choosing a red ball is more likely.

After this introduction to probability, we can look at probability of simple events and probability of complementary events.