A tree diagram is a helpful tool for determining theoretical or mathematical probabilities. Let's begin by examining the problem of tossing a fair coin. We'll focus on the number of heads that occur in a certain number of tosses. Note 7
A tree diagram for the toss of a single coin has two branches that represent the two possible outcomes of this random experiment. In this tree diagram, the red branch represents the outcome "heads" (H), and the blue branch represents the outcome "tails" (T):
For a single toss, the outcome is either heads or tails. Since we're looking at the number of heads that occur, the possible values from one toss are either 1 (heads) or 0 (tails).
We can extend the tree diagram to show more than one coin toss. Complete the exercise below to see how we construct the diagram. Try several rounds of two, three, and four tosses, and record your outcomes.