Chapter 11 Probability Worksheet Page 23
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PROBABILITY (Chapter 11)
MUTUALLY EXCLUSIVE OR DISJOINT EVENTS
In Chapter 1 we defined mutually exclusive sets.
If A and B are mutually exclusive events then P(A \ B) = 0
In a Venn diagram for
mutually exclusive
and so the addition law becomes
events, the circles for the
P(A [ B) = P(A) + P(B).
events do not overlap.
Mutually exclusive events have
no common outcomes.
A
B
U
Example 16
Self Tutor
A piece of fruit is randomly selected from a basket containing 8 apples and 12 oranges.
The event A represents selecting an apple, and O represents selecting an orange.
a
Are A and O mutually exclusive?
P(A \ O)
P(A [ O).
b
Find
i
P(A)
ii
P(O)
iii
iv
a
A piece of fruit cannot be an apple and an orange.
) A and O are mutually exclusive.
8
2
12
3
P(A) =
=
P(O) =
=
b
i
ii
20
5
20
5
20
P(A \ O) = 0
P(A [ O) =
= 1
iii
iv
20
CONDITIONAL PROBABILITY
If we have two events A and B, then
A j B is used to represent that ‘A occurs knowing that B has occurred’.
A j B is often read as ‘A given B’.
Example 17
Self Tutor
In a group of 25 students, 15 like chocolate milk (M) and 17 like iced coffee (C).
Two students like neither and 9 students like both. One student is randomly selected
from the class. What is the probability that the student:
a
likes chocolate milk
b
likes chocolate milk given that he or she likes iced coffee?
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