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This module introduces Venn diagrams as a method for solving some probability problems. This module is included in the Elementary Statistics textbook/collection as an optional lesson.
A
Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.
Suppose an experiment has the outcomes 1, 2, 3, ... , 12 where each outcome has an equal chance of occurring. Let event
and event
. Then
and
. The Venn diagram is as follows:
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Flip 2 fair coins. Let
= tails on the first coin. Let
= tails on the second coin. Then
and
.
Therefore,
.
.
The sample space when you flip two fair coins is
. The outcome
is in neither
nor
. The Venn diagram is as follows:
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Forty percent of the students at a local college belong to a club and
50% work part time.
Five percent of the students work part time and belong to a club. Draw a Venn diagram showing the relationships. Let
= student belongs to a club and
= student works part time.
If a student is selected at random find
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Questions & Answers
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Source:
OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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