F. Are \( A \) and B indppendent events? A Two events \( A \) and \( B \) are not independent because the occurrence of one affects the chance the other occurs. Numerically, \( P(A \mid B) \neq P(A) \), so events \( A \) and \( B \) are not independent. s Two events A and B are independent because the cccurrence of one does not affect the chance the other occurs. Numerically, \( P(A \mid B)=P(A) \), so events \( A \) and \( B \) are independent.

Understanding the foundation of probability is essential! In probability theory, two events are considered independent if knowing that one event occurred does not change the probability of the other event occurring. Mathematically, this is represented as \( P(A \cap B) = P(A) \cdot P(B) \). So, if you find that the multiplication rule holds true, you can confidently declare these events independent! Let's dive into a common pitfall! A frequent mistake occurs when people confuse conditional probabilities. Always double-check whether \( P(A \mid B) \) equals \( P(A) \). It might seem trivial, but if you mistake it, you could easily mislabel the relationship between two events! Ensuring clarity on what independence means can save you from some serious probability headaches.