1. The problem is to understand the difference between dependent and independent events in probability. 2. An event is a set of outcomes from a random experiment. Two events are called independent if the occurrence of one does not affect the probability of the other. 3. The formula for independent events $A$ and $B$ is: $$P(A \cap B) = P(A) \times P(B)$$ This means the probability of both events happening is the product of their individual probabilities. 4. Dependent events are events where the occurrence of one event affects the probability of the other. 5. For dependent events, the probability of both events happening is: $$P(A \cap B) = P(A) \times P(B|A)$$ where $P(B|A)$ is the probability of $B$ given that $A$ has occurred. 6. In simple terms, if knowing that one event happened changes the chance of the other event, they are dependent. 7. If knowing one event happened does not change the chance of the other, they are independent. This is the key difference between dependent and independent events.