The Science of Life

As promised last time , I am going to cover Baye's Theorem. If Tree diagram is the common name for Bayes Theorem.  Recall that conditional probability is given by $P(A \mid B) = \frac{P(A \wedge B)}{P(B)}$.   For tree diagrams, let's say that we have events A, B 1 , B 2 , B 3 , … (the reason we have multiple B's is because they all are within the same family of events) such that the events in the family of B are mutually exclusive and the sum of the probabilities of the events in the family of B are equal to 1. Then we have $$P(B_i \mid A)= \frac{P(B_i)*P(A \mid B_i)}{\sum_{m=1}^{n}[P(B_m)*P(A \mid B_m)]}$$  What this means is reliant on the tree diagram. If we are only looking at the sub-items of A, this is what the tree diagram would look like. If J has a probability of 100%, and P(C) and P(D) are not 0, then when we are trying to find the probability of any of the B's being true given that A is true, we have to set the probability of A to be t...