Conditional Probability Tree Diagram: Example, Statistical Note 2

A Tree Diagram is an important tool to visualize the events and their respective probabilities. I have taken an example from my statistical note 1 (Calculating the probability that a randomly selected person is a woman who is a vegetarian also) to show the process of drawing the probability tree diagram.

At the first step, there are two possible mutually exclusive or independent outcomes: women or men in the sample space of total training participants. The outcomes are independent because the selection of a woman does not depend on men. Let W be a simple event that a selected participant is a woman. The simple or marginal probability of the simple event W, denoted by P(W) is 0.40. It means that is 40 percent participants in the training are women. Another possible simple event is that the selected participant is a man, denoted by M and the simple or marginal probability of the event M denoted by P(M) is 0.60, that is 60 percent participants are men. These marginal probabilities at the first step are shown in the diagram, also referred to as the tree diagram 1.

Diagram 1: First step showing marginal probabilities

Once a woman is selected at the first step, there are two possible mutually exclusive dependent outcomes in the second step: vegetarian or non-vegetarian. Let V/W be an event that among the women participants, one is a vegetarian (V).  Now, the conditional probability of V/W denoted by P(V/W) is 0.75, that is 75 percent women participants are vegetarians. Likewise, let NV/W be an event that among the women participants, one is a non-vegetarian (NV).  The conditional probability of NV/W denoted by P(NV/W) is 0.25, that is 25 percent women participants are non-vegetarians. Similarly, conditional probabilities that a participant selected among women is a vegetarian or a non-vegetarian can be shown using a tree diagram 2.

 

Diagram 2: First and second steps showing marginal and conditional probabilities