Probability of Rainfall in a City?

📌 CONCEPT: The actual probability of rainfall tomorrow can be found by combining the given probabilities using the rules of probability.

📐 RULE / FORMULA: According to the rule of total probability, if we have two events A and B, and the probability of B given A is P(B|A), then the probability of A and B occurring is given by P(A and B) = P(A) * P(B|A).

💡 WORKED EXAMPLE: Given that there is a 60% chance of rainfall (event R) and a 20% chance of atmospheric pressure dropping below 1000 mb (event P), and the probability of rainfall given that atmospheric pressure drops below 1000 mb is 80%, we can find the actual probability of rainfall as follows: P(R) = P(R|P) * P(P) = 0.8 * 0.2 = 0.16 or 16%.

⚠️ COMMON MISTAKE: Students often forget to apply the rule of total probability and simply add the probabilities of the two events, resulting in an incorrect answer.