Question

For events A and B, the following probabilities are known:

Pr[A∪B]=0.8Pr[A]=0.5
What is the value of Pr[B] if A and B are disjoint?P if A

Answer 1

Anybody that can help me with this?

Answer 2

The rule for unions states: \(P(A \cup B)=P(A)+P(B)-P(A\cap B)\)

If A and B are disjoint, they are mutually exclusive. If they are mutually exclusive, then \(P(A \cap B)=0\). This means that the above formula reduces to:

\(P(A \cup B)=P(A)+P(B)\). So you just need to solve for \(P(B)\):

\(P(B)=P(A\cup B)-P(A)\)

Answer 3

So Pr(B) is 0?