Let $A$, $B$, and $C$ be three events in a sample space. If $A$ and $B$ are mutually exclusive, and $P(A) = 0.2$, $P(B) = 0.3$, and $P(C) = 0.4$, and given that $A$ and $C$ are ind... Let $A$, $B$, and $C$ be three events in a sample space. If $A$ and $B$ are mutually exclusive, and $P(A) = 0.2$, $P(B) = 0.3$, and $P(C) = 0.4$, and given that $A$ and $C$ are independent, what is $P(A \cup B \cup C)$ if $B$ and $C$ are also independent? Read more

Understand the Problem

The question asks us to compute the probability of the union of three events A, B, and C, given certain probabilities and independence/mutual exclusivity conditions. Specifically, A and B are mutually exclusive, A and C are independent, and B and C are independent. We are given P(A), P(B), and P(C). We need to calculate P(A ∪ B ∪ C). The approach will involve using the inclusion-exclusion principle and the properties of independence and mutual exclusivity to simplify the calculation.