The Addition Rule on a Tree Diagram
(KS3, Year 7)
The LessonA tree diagram shows all the possible outcomes of an event and their probabilities. We can find the probability of one event or another event.
A Single Coin TossA single coin toss can be shown on a tree diagram.
The probability of each event can be read from each branch:
- The probability of getting Heads is 1⁄2.
- The probability of getting Tails is 1⁄2.
The probability of Heads or Tails is found by adding their probabilities.
1⁄2 + 1⁄2 = 1
How to Find the Probability of an Event or Another Event on a Tree DiagramThe addition rule can be used for more complicated tree diagrams. The tree diagram below is for a double coin toss.
QuestionWhat is the probability of both tosses landing the same side up?
Find the event given in the question. The event is the coin landing the same side up on both tosses. There are two ways this can happen:
- Heads and Heads
- Tails and Tails
Add the probabilities for these outcomes.
1⁄4 × 1⁄4 = 2⁄4
Answer:The probability of getting Heads and Heads or Tails and Tails is 1⁄2. We can also express this as a number (0.5) or a percentage (50%).
Lesson SlidesThe slider below another real example of using the addition rule on a tree diagram. Open the slider in a new tab
What Is Probability?A probability is a measure of how likely (how probable) an event is to happen. A probability is expressed as a number between 0 (impossible) and 1 (certain). The formula for finding a probability is shown below:
A Useful CheckThere is a useful way to check that the probabilities on a tree diagram are all correct. The probabilities of each final outcome add up to 1:
- Do you disagree with something on this page?
- Did you spot a typo?