MDM4U Mutually Exclusive Events
Mutually exclusive or disjoint events are events that cannot occur at
the same time.
𝐴∩𝐵 = ∅
For mutually exclusive events A and B holds:
𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)
Example
If a committee of 5 is to be chosen randomly from 6 males and 8
females, what is the probability that the committee is either all male or
all female?
Solution
A = “committee is all male“
B = “committee is all female“
𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵)
=
(6)
5
14
(5)
6
+
=
+
2002
≈ 0.03
(8)
5
14
(5)
56
2002
Non-mutually exclusive events: Events that can occur at the same time.
𝐴∩𝐵 ≠ ∅
For non-mutually exclusive events A and B holds:
𝑃(𝐴 ∪ 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 ∩ 𝐵)
Example
There is a group of 15 teachers: 8 female, 2 of the teachers are Russian
in origin, one Russian teacher is a female. What is the probability that
randomly selected teacher is either Russian or a female?
𝑃(𝑅 ∪ 𝐹 ) = 𝑃(𝑅 ) + 𝑃(𝐹 ) − 𝑃(𝑅 ∩ 𝐹 )
=
=
2
15
9
15
3
= .
5
+
8
15
−
1
15
Example
What is the probability of rolling a sum greater than 7 or doubles with a
pair of dice?
Dice Chart:
1
2
3
4
5
6
1
2
3
4
5
6
7
2
3
4
5
6
7
8
3 4 5 6
4 5 6 7
5 6 7 8
6 7 8 9
7 8 9 10
8 9 10 11
9 10 11 12