Question

A and B are mutually exclusive events suchthat P(A)=0.4 and P(B)=0.5. What is the probability that either A or B does not occur.

Answer 1

Step-by-step explanation:

P(A and B) = 0 because the two events are mutually exclusive

P(A or B) = P(A) + P(B) - P(A and B) = 0.4 + 0.5 - 0 = 0.9

P(Not A) = 1 - P(A) = 0.6

P(Not B) = 1 - P(B) = 0.5

P(not (A or B)) = 1 - P(A or B) = 0.1 (this could also be solved using DeMorgans law)

Finally, solve the last one by using the law of total probability:

P(A and (not B)) = P(A) - P(A and B) = 0.4 - 0

I will note that these can all be solved intuitively by using a Venn diagram.