Statistics for Business: Decision Making and Analysis, 3rd Edition

... gold nodes identify these viewers. To find the probability of this combination, follow the branches and multiply the probabilities along the way.

$$P\left(\text{Using Spotify} and \text{See} \text{ads}\right)=0.50\times 0.50=0.25$$

This is exactly the calculation of this probability we got from the Multiplication Rule, only now it is laid out in a tree.

The events at the far right of the probability tree are disjoint. These final nodes, or leaves as they are sometimes called, identify all the possibilities. Hence, the probabilities of the leaves of the tree sum to 1.

$$\begin{array}{l}0.15\times 0.67+0.15\times 0.33+0.35\times 0.80+0.35\times 0.20\\ +0.50\times 0.50+0.50\times 0.50=1\end{array}$$

We can use these final outcomes to find other probabilities. For example, what’s the probability that a randomly chosen viewer sees ads? For this, add the probabilities ...