Conditional Probability in Real Life

📌 CONCEPT: Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted by P(A|B) and is used to determine the likelihood of an event happening when we have additional information about the situation.

📐 RULE / FORMULA: The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B occurring, and P(B) is the probability of event B occurring.

💡 WORKED EXAMPLE: In this scenario, let event A be 'a person develops diabetes' and event B be 'a person has a family history of diabetes'. Given that 10% of people with a family history will develop diabetes, and 1% of people without a family history will develop it, we can calculate the conditional probability as follows: 1. P(A ∩ B) = 10% = 0.1 2. P(B) = 70% = 0.7 3. P(A|B) = P(A ∩ B) / P(B) = 0.1 / 0.7 ≈ 0.143 or 14.3%

⚠️ COMMON MISTAKE: Students often forget to use the correct formula and instead try to calculate the probability of event A occurring without considering the additional information provided by event B.