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Topic: Mutually Exclusive and Complementary Events


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Subject:   Mutually Exclusive and Complementary Events
Author: tackweed
Date: Oct 26 2004
In Washington State we have our 7th grade assessment of student learning
(called the WASL) which is supposedly based on Essential Academic Learning
Requirments (EALRs). In the latest iteration, we have Grade Level Expectations
(GLEs). One of these new requirments is the inclusion of the concepts (and
terms) of COMPLEMENTARY and MUTUALLY EXCLUSIVE events to independent events.

The problem we will be facing is how to introduce the three concepts and
vocabulary (complementary, independent, and mutually exclusive events) to 7th
graders.  At the bottom of this message are listed the various state EALRs,
GLEs, and the test item specifications for these topics.

The following list is the resources I have been able to find on-line. I would
appreciate any supplementary materials, approaches and/or experiences for
incorporating these concepts at this level.

Thanks,

Jeff

==============================
"Mutually Exclusive vs. Independent

It is not uncommon for people to confuse the concepts of mutually exclusive
events and independent events.

    •Exclusive Events If event A happens, then event B cannot, or
vice-versa.
    •Events The outcome of event A has no effect on the outcome of event B.

So, if A and B are mutually exclusive, they cannot be independent. If A and B
are independent, they cannot be mutually exclusive."

http://mathcentral.uregina.ca/QQ/database/QQ.09.00/marje1.html  Explanation with
diagrams, i.e., table of outcomes and Venn diagram


complementary events
http://www.ex.ac.uk/cimt/mepres/book7/bk7i21/bk7_21i4.htm  Definition with some
interactive problems
=============================

Washington State  EALRs, GLEs, and the test item specifications for these
topics:

EALR 1.4.1 Understand the concepts of complementary, independent, and mutually
exclusive events.

Grade Level Expectations (suggested)

•Determine and explain when events are mutually exclusive (e.g., your grade on a
test is an A, B, or C). [CU, MC]
•Determine and explain when events are complementary (e.g., a person awake or
asleep, you pass or fail a test, coin throw - heads or tails). [CU, MC]
•Identify or explain when events are complementary, mutually exclusive, or
neither (e.g., spinning a 4 or a 5 but with the possibility of spinning 1, 2, 3,
or 6) and explain. [CU]

EALR 1.4.2 Understand and apply the procedures for determining the probabilities
of multiple trials.  

Grade Level Expectations (suggested)

•Calculate the probabilities of independent or mutually exclusive outcomes or
events.
•Calculate the probability of an event given the probability of its
complement.


Test Item Characteristics:
a) Items may ask students to identify mutually exclusive or complementary
events.
b) Items may ask students to explain when events are complementary, mutually
exclusive, or neither.
c) Items may ask students to list the outcomes of mutually exclusive or
complementary events.
d) Items may ask students to identify or determine probabilities of experiments
and situations including complementary or mutually exclusive events as a ratio,
decimal, or percent.
e) Items may ask students to revise a game with unequal probabilities to make it
a fair game.


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