Mathematics

Independence is about whether knowing one event happened changes the probability of the other. The key insight is to check if $P(A \cap B) = P(A) \cdot P(B)$—if this equation holds, the events are independent; if not, they're dependent. Calculate what the intersection should be if they were independent, then compare it to what you're actually given.

Independence is about whether knowing one event happened changes the probability of the other. The key insight is to check if $P(A \cap B) = P(A) \cdot P(B)$—if this equation holds, the events are independent; if not, they're dependent. Calculate what the intersection should be if they were independent, then compare it to what you're actually given.