Let’s say that you saw dark clouds today. There is a 70% cha…
Let’s say that you saw dark clouds today. There is a 70% chance of seeing dark clouds today given that it will rain tomorrow (from historical data). There is a 20% chance of seeing dark clouds today given that it won’t rain tomorrow (again from historical data). There is a 50% chance of seeing dark clouds regardless of whether or not it will rain. The current knowledge without any extra information is that there is a 30% chance of rain tomorrow. What is the updated probability of rain tomorrow given that we saw dark clouds today? Hint: Let A be the event that it will rain tomorrow and B be the event that you observed dark clouds today. You need to find P(A|B). Use the tree diagram and Bayes theorem.