The Bonferroni Inequality states that for any events A, B, and C:
$$
P(A \cup B \cup C) \geq P(A) + P(B) + P(C) - P(A \cap B) - P(A \cap C) - P(B \cap C)
$$
Now, let's apply this inequality to the given events $A$, $B$, and $C$:
$$
P(A \cup B \cup C) \geq P(A)
Show more…