Question

Let $E , F$ and $G$ be three events having probabilities
$P(E)=\frac{1}{8}, P(F)=\frac{1}{6}$ and $P(G)=\frac{1}{4}$, and let $P(E \cap F \cap G)=\frac{1}{10}$.
For any event $H$, if $H ^{ C }$ denotes its complement, then which of the following statements is(are) TRUE?

• A. $P\left(E \cap F \cap G^{C}\right) \leq \frac{1}{40}$
• B. $P\left(E^{C} \cap F \cap G\right) \leq \frac{1}{15}$
• C. $P(E \cup F \cup G) \leq \frac{13}{24}$
• D. $P\left(E^{C} \cap F^{C} \cap G^{C}\right) \leq \frac{5}{12}$

Answer 1

Answer: (A), (B), (C)

$P\left(E \cap F \cap G^{C}\right) \leq \frac{1}{40}$

Answer 2

(A)$P\left(E \cap F \cap G^{C}\right) \leq \frac{1}{40}$
(B) $P\left(E^{C} \cap F \cap G\right) \leq \frac{1}{15}$
(C) $P(E \cup F \cup G) \leq \frac{13}{24}$