Conditional Probability Puzzle?

📌 CONCEPT: Conditional probability is the probability of an event occurring given that another event has already occurred, which can be calculated using the formula P(A|B) = P(A ∩ B) / P(B).

📐 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: Consider a bag containing 3 red, 5 blue, and 2 green balls. The probability of drawing a non-blue ball first is 8/10. The probability of drawing a blue ball second, given that the first ball was not blue, is P(B2|NB1) = P(B2 ∩ NB1) / P(NB1) = (5/10) * (5/9) / (8/10) = 25/72.

⚠️ COMMON MISTAKE: Students often forget to update the total number of balls after the first draw, which can lead to incorrect calculations for conditional probability.