Probability of Unrelated Events

📌 CONCEPT: In probability, the probability of unrelated events occurring together is found using the concept of independent events, where the occurrence of one event does not affect the probability of the other event occurring.

📐 RULE / FORMULA: The rule for finding the probability of event A occurring and event B not occurring is given by P(A ∩ B') = P(A) * (1 - P(B)), where P(A ∩ B') represents the probability of A occurring and B not occurring, P(A) is the probability of event A occurring, and P(B) is the probability of event B occurring.

💡 WORKED EXAMPLE: Let's say the probability of event A occurring is 0.6 and the probability of event B occurring is 0.3. We need to find P(A ∩ B'). Using the formula, we have P(A ∩ B') = 0.6 * (1 - 0.3) = 0.6 * 0.7 = 0.42.

⚠️ COMMON MISTAKE: Students often make the mistake of assuming that the probability of A occurring and B not occurring is simply the difference between the probabilities of A and B, i.e., P(A ∩ B') = P(A) - P(B). This is incorrect because it does not take into account the fact that event B may still occur even though the probability of its occurrence is low.