The Addition Rule on a Tree Diagram
Probabilities of an Event or Another Event on a Tree Diagram
We can find the probability of one event or another event.
A Single Coin Toss
A 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.
Imagine we wanted to find the probability of getting Heads or Tails.
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 Diagram
The addition rule can be used for more complicated tree diagrams.
The tree diagram below is for a double coin toss.
What is the probability of both tosses landing the same side up?
To find the probability of an event or another event, add across the branches.
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
We are finding the probability of Heads and Heads or Tails and Tails. These are the top branches and the bottom branches of the tree diagram.
Add the probabilities for these outcomes.
1⁄4 × 1⁄4 = 2⁄4
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%).
The slider below another real example of using the addition rule on a tree diagram.Open the slider in a new tab