Posted by Anjali Kaur on Jul 17, 2020
Probability

What is Probability?

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur, that is, how likely they are to happen.

Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value lies between zero and one. Probability has been introduced in Maths to predict how likely events are to happen.

Table of content:

Meaning of probability

Random Experiment

Sample space

Events

Meaning of Probability

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur. that is, how likely they are to happen. Probability can range between 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event. The probability of all the events in a sample space sums up to 1.

For example, when we toss a coin, either we get Head OR Tail, only two possible outcomes are possible (H, T). But if we toss two coins in the air, there could be three possibilities of events to occur, such as both the coins show heads or both shows tails or one shows heads and one tail, i.e.(H, H), (H, T),(T, H) and (T, T).

Random Experiment

An experiment whose outcomes cannot be predicted or determined in advance is called a random experiment. For example, in the tossing of a coin, one is not sure if a head or a tail will be obtained so, it is a random experiment. Similarly, rolling an unbiased die and drawing a card from a well-shuffled pack of playing cards.

Sample Space

Sample Space means the set of all possible outcomes of a random experiment. For example, in tossing a coin, the sample space will be S = {H, T}.

Test Yourself:

What is the sample space of a coin tossed two times?

Event

The event stands for a subset of the sample space-related with a random experiment. For example, in a random experiment of throwing a die, Sample space, S = {1,2,3,4,5,6}. So the subset of S has 26= 64 subsets. (A set with n elements has 2 n subsets.)

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