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# Basic Terminology

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#### Basic Terminology - Lesson Summary

Probability is defined as the likelihood of something occurring.

Activity 1:

Find the sum of the measures of the angles of some quadrilaterals.

The sum of the measures of the angles of a quadrilateral is 360°.
If the same activity is performed for any quadrilateral, the result will be the same.

Activity 2:

Measure the sides of some equilateral triangles.

The sides of an equilateral triangle are equal.
If the same activity is performed any number of times for any equilateral triangle, the result is same.

These types of activities are called experiments.

In these experiments, the result can be predicted. There are some experiments, where we cannot predict the results.

Consider an experiment where a die is rolled ten times. Every time, a result is obtained.

Experiments in which the result cannot be predicted are called random experiments.

A random experiment is an experiment where there are more than one possible results and it is not possible to predict the result in advance.

The possible result of an experiment is called its outcome.

Ex:

The outcomes of rolling a die are 1, 2, 3, 4, 5, 6.
The outcomes of tossing a coin are heads and tails.

A random experiment can have any number of predictable outcomes.

The set of all the outcomes of a random experiment is called sample space. It is denoted by S.
The sample spaces of rolling a die and tossing a coin are

Sample space (S) = {1, 2, 3, 4, 5, 6}

Sample space (S) = {H, T}

An element of a sample space is called a sample point. In other words, every outcome of a random experiment is also called a sample point.

Activity of tossing two coins

Each coin can turn up either heads or tails.

Therefore, the possible outcomes may be: Heads on both the coins, Heads on the first coin and tails on the second coin, Tails on the first coin and heads on the second coin, And tails on both the coins.

Therefore, the sample space (S) of the experiment is {HH, HT, TH, TT}.

The outcomes of this experiment are the ordered pairs of the outcome of the first coin and the outcome of the second coin.

In set builder form, this can also be written as:

S = {(x,y): x is the outcome of the first coin and y is the outcome of the second coin}

A collection of the outcomes of a sample space is called an event.

A subset of a sample space is called an event.

Examples of event: {HH}, {HH, TT}, {TH, TT}...