What is P(A ∪ B)? Original Problem in Description.

Question

Suppose A and B are mutually exclusive events in a sample space S, C is another event in S, A ∪ B ∪ C = S, and A and B have probabilities 0.1 and 0.5, respectively.

What is P(A ∪ B)?

Answer 1

Since A and B are mutually exclusive the P(A intersection B)=0. Hence,

P(A union B)= P(A)+P(B)-P(A intersection B)=P(A)+P(B)=0.1+0.5=0.6.