The LessonA tree diagram shows all the possible outcomes of an event and their probabilities. For example, it shows us the probability of a single event, such as a single coin toss.
A Single Coin TossA single coin toss can be shown on a tree diagram.To find the probability of an event, read the probability on each branch:
- The probability of getting Heads is 1⁄2.
- The probability of getting Tails is 1⁄2.
A Double Coin TossA double coin toss can be shown on a tree diagram.Imagine we wanted to find the probability of getting Heads and Heads in a double coin toss.
How to Find the Probability of an Event and Another Event on a Tree Diagram
QuestionWhat is the probability of getting Heads and Heads in a double coin toss?
Find the event given in the question. The event Heads and Heads is found in the top branches.
Find the probabilities along the branches for this event. The probabilities along the branches are 1⁄2 on the left branch and 1⁄2 on the right branch.
Multiply the probabilities along the branches.
1⁄2 × 1⁄2 = 1⁄4
Simplify the fraction if possible. (The fraction in our example is already as simple as possible).
Answer:The probability of getting Heads and Heads is 1⁄4.
Using notation, if H is the event of a Heads coming up, the probability of the event happening twice is P(HH). We can also express this as a number (0.25) or a percentage (25%).
Finding All Probabilities from a Tree DiagramAll the probabilities in a tree diagram can be found in the same way. Consider the tree diagram for a double coin toss. If we multiply across all branches, we find the probability of each outcome.
Note: If we add the probabilities of each outcome, they add to 1.
1⁄4 + 1⁄4 + 1⁄4 + 1⁄4 = 1