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What is a random event?
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Brandon Hodgson
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Creative Commons Attribution License 2.0
1 What is a random event?
An event is a set of outcomes (a subset of the sample space) to which a probability is assigned (Wikipedia
2006a). Typically, any subset of the sample space is an event (i.e. all elements of the power set of the sample
space are events) (Wikipedia 2006a).
Example 1
This example is extracted from (Wikipedia 2006a). If we assemble a deck of 52 playing cards with
two jokers, and draw a single card from the deck, then the sample space is a 54-element set, as
each individual card is a possible outcome. An event, however, is any subset of the sample space,
including any single-element set (an elementary event, of which there are 54, representing the 54
possible cards drawn from the deck), the empty set (which is dened to have probability zero) and
the entire set of 54 cards, the sample space itself (which is dened to have probability one). Other
events are proper subsets of the sample space that contain multiple elements. So, for example,
potential events include:
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"Red and black at the same time without being a joker" (0 elements),
"The 5 of Hearts" (1 element),
"A King" (4 elements),
"A Face card" (12 elements),
"A Spade" (13 elements),
"A Face card or a red suit" (32 elements),
"A card" (54 elements).
Since all events are sets, they are usually written as sets (e.g. {1, 2, 3}), and represented graphically using
Venn diagrams (illustrations used in the branch of mathematics known as set theory)(Wikipedia 2006a, b).
Venn diagrams are particularly useful for representing events because the probability of the event can be
identied with the ratio of the area of the event and the area of the sample space (Wikipedia 2006a). An
example of a Venn diagram is shown in gure 1 (Wikipedia 2006).
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Figure 1
(Wikipedia 2006)
Figure 1: A Venn diagram of an event. B is the sample space and A is an event. By the ratio of their
areas, the probability of A is approximately 0.4 (Wikipedia 2006).
Exercise 1
(Solution on p. 3.)
When sending packets of information through a channel, does receiving erroneous packet qualies
as a random event?
References:
Ali M. "Probabilistic Sytems Analyses: Part I," University of the Witwatersrand, 2000.
Wikipedia. "Event (probability theory)," Wikimedia Foundation Inc, http://en.wikipedia.org/wiki/Event_%28probab
, Last accessed 17 February 2006.
Wikipedia. "Venn diagram," Wikimedia Foundation Inc, http://en.wikipedia.org/wiki/Venn_diagram2
, Last accessed 17 February 2006.
Author of assignment 3: Brandon Hodgson
Author of assignment 1: Mphekwane (Eddie) Mamahlodi
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http://en.wikipedia.org/wiki/Event_%28probability_theory%29
http://en.wikipedia.org/wiki/Venn_diagram
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Solutions to Exercises in this Module
Solution to Exercise (p. 2)
Yes. One cannot predict when exactly a packet of information will be distorted along the channel. Thus
randomly, one bit in the information packet may be received wrongly.
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