How do you create a tree diagram for rolling two dice?

To create a tree diagram for rolling two dice, draw branches for each possible outcome of the first and second dice.

Start by drawing a single point, which represents the initial state before any dice are rolled. From this point, draw six branches, each representing one of the possible outcomes of rolling the first die (1, 2, 3, 4, 5, and 6). Label each branch with the corresponding number.

Next, from the end of each of these six branches, draw another set of six branches. These new branches represent the possible outcomes of rolling the second die. Again, label each branch with the numbers 1 through 6.

Now, you should have a tree diagram with a total of 36 end points (6 outcomes from the first die multiplied by 6 outcomes from the second die). Each path from the starting point to an end point represents a unique combination of outcomes from rolling the two dice. For example, one path might go from the starting point to a branch labelled "3" (first die) and then to a branch labelled "5" (second die), representing the outcome (3, 5).

This tree diagram helps you visualise all possible outcomes and is useful for calculating probabilities. For instance, if you want to find the probability of rolling a sum of 7, you can count the paths that result in this sum and divide by the total number of paths (36).