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Sample Space Experiment & Event

Experiment, Sample Space & Event Online Tutoring / Homework Help

Experiment can be of two types: Deterministic experiment and non-deterministic or random experiment.

An experiment whose outcome is unique is called a Deterministic experiment.

And an experiment whose outcome is not unique and cannot be calculated in advance, but is one of the set of possible outcomes, then it is called a random experiment.


The set of all possible outcomes of a random experiment is called the sample space. Sample space is denoted by S

For example, when we toss a coin there can be two possible outcomes, head or tail. So the sample space of this experiment will be, S = {H, T}

A few more examples of sample space are:

In the experiment of throwing a pair of dice, S = {(1,1), (1,2), (1,3), (1,4), (1,5), (1,6), (2,1), (2,2),...... (6,1), (6,2), (6,3), (6,4), (6,5), (6,6)}

In the experiment of tossing two coins simultaneously,
S = {HH, HT, TH, TT}


An event is a subset of the sample space. It is denoted by E. For example, {a tail} in the experiment of tossing a coin is an event. There are two types of events: Simple event and compound event.

If an event has only one element of the sample space then it is called a simple event.

For example, in S = {2, 5, 6, 9} if the event is set of elements greater than 6 then E = {9} is a simple event.

If an event has more than one elements of the sample space then it is called a compound event. For example, in the experiment of tossing two coins together the sample space will be, S = {HH, HT, TH, TT} if the event has two of the same side then E = {HH, TT} is a compound event.

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