Question

If $C_1$ and $C_2$ are subset of sample space S. Then which is correct:

• A. $P(C_1 \cap C_2) \ge P(C_1)$
• B. $P(C_1 \cap C_2) \ge P(C_2)$
• C. $P(C_1 \cap C_2) \le P(C_1 \cup C_2)$
• D. $P(C_1 \cup C_2) \ge P(C_1) + P(C_2)$

Hint:

To visualize these set relationships quickly, use a Venn Diagram:
- The overlapping region (Intersection) is always smaller than or equal to either individual circle.
- Both circles combined (Union) always cover an area larger than or equal to the overlapping region.

Answer 1

The Correct Option is C