Question

Let E, F and G be events such that $P(E|G) = 0.05$ and $P(F|G) = 0.05$ which of the following statement must be true?

• A. $P(E \cap F|G) = (0.05)^2$
• B. $P(\overline{E} \cap \overline{F}|G) \ge 0.90$
• C. $P(E \cup F|G) \le 0.05$
• D. $P(E \cup F|\overline{G}) \ge 1 - (0.05)^2$

Hint:

This is an application of Boole's Inequality. For any events, $P(\cup A_i) \le \sum P(A_i)$. By finding the upper bound of the "bad" events (E or F), you automatically find the lower bound of the "good" event (neither E nor F).

Answer 1

The Correct Option is B