4.69 Draw a different tree diagram for the same setting.
Refer to the previous two exercises. Draw a tree diagram to illustrate the probabilities in a situation in which you first identify the gender of the student and then identify the type of institution attended. Explain why the probabilities in this tree diagram are different from those that you used in the previous exercise.
4.69
The tree diagrams are different because each branch on the tree is a conditional probability given the previous branches. So by rearranging the order of the branches, we are necessarily changing the probabilities (assuming the events are not independent).