The Lesson
A 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 Toss
A 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 Toss
A 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
Question
What is the probability of getting Heads and Heads in a double coin toss?Step-by-Step:
1
Find the event given in the question.
The event Heads and Heads is found in the top branches.
2
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.
3
Multiply the probabilities along the branches.
1⁄2 × 1⁄2 = 1⁄4
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 Diagram
All 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