High School Probability and Statistics/Events, Sample Spaces, and Probability

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Probability:[edit]

Introduction:[edit]

Consciously or unconsciously all of us sometimes use phrases like: ‘most likely’, ‘almost uncertain’, ‘most probably’, ‘no chance at all’, etc. If we read these carefully, we will find that all of them involve an element of uncertainty. The measure is called the theory of probability.

Some Basic Terms and Concepts:[edit]

Experiment :[edit]

A process that results in some well-defined outcome is known as an experiment. For example:

  1. (i) When a coin is tossed, we shall be getting either a head or a tail i.e its outcome is a head or a tail, which is well-defined.

Random Experiment:[edit]

Random experiment means all the outcomes of the experiment are known in advance, but any specific outcome od he experiments is not known in advance. For examples:

  1. (i) Tossing a coin is a random experiment because there are only two possible outcomes, head or tail, and these outcomes are known well in advance. But the specific outcome of the experiment i.e whether a head or a tail is not known in advance

Sample Space:[edit]

The set of all possible outcomes of an experiment is called sample pace and is, in general, denoted by letter S For example: (i) When a coin and a dice are tossed together, the corresponding sample space for the random experiment is as given below:

S={(H,1), (H,2), (H,3), (H,4), (H,5), (H,6),(T,1), (T,2), (T,3), (T,4), (T,5), (T,6)}.

An Event:[edit]

An outcome of a random experiment is called an event. In other words, an event is something that happens. On tossing a coin, the possible outcome is head (H) or a tail (T). Here, getting ahead or a tail is an event of the experiment.