Probability tree
A useful way to organize information about events in a probability space is by drawing a probability tree. Here the branches corrsepond to events, and the edges are weighted by the corresponding conditional probabilities.
Consider the experiment where we choose coin a 1/3 of the time, and coin b 2/3 of the time, and where coin a lands heads 3/4 of the time and coin b lands heads 1/2 of the time.
We can draw a tree to organize these events into a tree:
The vertices in the tree represent events; the event is a child of if . The number on the edge from to is the conditional probability of given .
The probability of an event in the tree can be found by multiplying the probabilities on the path leading to that event. This comes from the definition of conditional probability: if then .
