If $A, B, C$ are three arbitrary events sach that $P(A)=P(B)=P(C)=\frac{1}{4}$. $P(A \cap B)=P(B \ca

Question

If $A, B, C$ are three arbitrary events sach that $P(A)=P(B)=P(C)=\frac{1}{4}$. $P(A \cap B)=P(B \cap C)=0$ and $P(A \cap C)=\frac{1}{8}$, then the probability that at least one of $A, B, C$ occurs is

Professor PC Thomas Classes · Answer

$P(A\cup B\cup C) = \sum P(A) - \sum P(A\cap B) + P(A\cap B\cap C) = \frac{3}{4} - \frac{1}{8} + 0 = \frac{5}{8}$.