1.5. Mutually Inclusive Events http://www.ck12.org
Example B
What is the probability of choosing a number from 1 to 10 that is less than 5 or odd?
A={ 1 , 2 , 3 , 4 }
P(A) =probability of selecting a number less than 5P(A) =4
10
P(A) =
2
5
B={ 1 , 3 , 5 , 7 , 9 }
P(B) =probability of selecting a number that is oddP(B) =5
10
P(B) =
1
2
P(A∩B) =
2
10
P(A∩B) =
1
5
P(A∪B) =P(A)+P(B)−P(A∩B)
P(A∪B) =
2
5
+
1
2
−
1
5
P(A∪B) =
4
10
+
5
10
−
2
10
P(A∪B) =
7
10
Notice in the previous 2 examples how the concept of double counting was incorporated into the calculation by
subtracting theP(A∪B). Let’s try a different example where you have 2 events happening.
Example C
2 fair dice are rolled. What is the probability of getting a sum less than 7 or a sum less than 4?
P(A) =probability of obtaining a sum less than 7