Probability Tree Diagram

Tags

math

Are a way to plot the likelihood of two or more events.

The tree is a binary tree with each branch representing the two possibilities of the event happening or not. Subsequent sub-branches expand on the likelihood of separate events.

For example

The probability that it rains on any given day in march is 0.4. If it is raining the probability that tom gets a lift is 0.8 and if it is not raining the probability is 0.5. Draw a tree diagram for this.

\begin{figure}
  \centering
\begin{verbatim}
	 0.8
	/
       /
      /\
     /  \
    0.4  0.2
   /
   \
    0.6  0.5
     \  /
      \/
       \
	\
	 0.5
\end{verbatim}
  \caption{A probability tree for two events, the likelihood of it raining and the
likelihood of Tom taking a car.}
  \label{fig:prob-tree}
\end{figure}

An example probability tree can be seen in fig:prob-tree. From this we can see the likelihood of Tom taking a car given it's raining is \(0.8\).