Question

If $A$ and $B$ are two events of a random experiment such that $P(\bar{A}) = 0.3$, $P(B) = 0.4$ and $P(A \cap \bar{B}) = 0.5$, then $P(A \cup B) = \_\_\_\_\_\_\_$

• A. 1
• B. 0.9
• C. 0.5
• D. 0.6

Hint:

Using a Venn diagram makes this very intuitive.
The region $A \cup B$ can be written as the disjoint union of $(A \cap \bar{B})$ and $B$.
Therefore: $P(A \cup B) = P(A \cap \bar{B}) + P(B) = 0.5 + 0.4 = 0.9$.
This requires only a single addition step.

Answer 1

The Correct Option is B