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

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

anonymous · Answer

Anybody that can help me with this?

kirbykirby · Answer

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

anonymous · Answer

So Pr(B) is 0?