Question

For any two possible events $A$ and $B$ the expression $P\left(\frac{A}{A \cup B}\right)$ is always equal to

• A. $\frac{P(A \cup B)-P(B)}{P(A \cup B)}$
• B. $\frac{P(A \cup B)-P(A)}{P(A \cup B)}$
• C. $\frac{ P ( A \cup B )- P ( B )+ P ( A \cap B )}{ P ( A \cup B )}$
• D. $\frac{P(A \cup B)+P(B)-P(A \cap B)}{P(A \cup B)}$

Answer 1

Answer: (C)

$\frac{P(A \cap(A \cup B))}{P(A \cup B)}=\frac{P(A)}{P(A \cup B)}=\frac{P(A \cup B)-P(B)+P(A \cap B)}{P(A \cup B)}$.