Sample Space

What is sample space?
Sample space is generally defined as the set of all possible outcomes of a random experiment. A sample
space may generally contain number of outcomes which depends on the experiment carried out.
On tossing a coin the sample space is given by,
The sample space is S = (H, T).
On tossing a die the sample space is given by,
The sample space is given by S = (1, 2, 3, 4, 5, 6).
Sometimes the sample space is easy to determine, but whereas in some cases they are difficult to
determine in such cases tree diagrams are used.
Any subset of the sample space is called as the event.
Sample Size
Sample size can be defined as the number of participants or observations considered under the study.
This is generally denoted as n. The size of the sample usually depends on two properties.

  1. The prediction of the estimates.
  2. The measure to arrive at the conclusion.
    Sample space and events particularly the relationship among the events is generally depicted by using
    the Venn diagrams.
    Since events are the subsets obtained from the sample space, we can talk about some of the operations
    of the events.
    If E and F are the events,
    Then their commutativity is given by,
    E ∪ F = F ∪ E, E ∩ F = F ∩ E
    Associativity can be given by,
    (E ∪ F) ∪ G = E ∪ (F ∪ G), (E ∩ F) ∩ G = E ∩ (F ∩ G)
    Distributivity is,

(E ∪ F) ∩ G = (E ∩ G) ∪ (F ∩ G), (E ∩ F) ∪ G = (E ∪ G) ∩ (F ∪ G)
A simple tree diagram below shows how the sample space is taken from the tree diagram.


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