# The 'Or' Rule for Probability from a Tree Diagram

The tree diagram below represents tossing a coin.

The 'or' rule of probability lets us find the probability that one event or another event occurs. For example, the probability of getting a Head or a Tail in a coin toss.

To do this, add the probabilities of each event to find the probability that either of them occur.

# How to Use the 'Or' Rule for Probability from a Tree Diagram

Question: What is the probability of getting a Head or a Tail?

Step 1: Find the probability of one event.
The probability of getting a Head, P(H), is:

Step 2: Find the probability of the other event.
The probability of getting a Tail, P(T), is:

Step 3: Add the probabilities together, and simplify if necessary.

The probability of tossing a Head or a Tail is 1.

# A Real Example of How to Use 'Or' Rule of Probability from a Tree Diagram

The above example was very simple, as it looked at the tree diagram for a single event. When there are sequential events, it becomes more complicated.

For example, a coin can be tossed twice.

Using the 'and' rule of probability, the probability of each of the four outcomes can be found:

The 'or' rule can then be used to find the probability that either of several outcomes occur.

Question: What is the probability of getting Head, Head or Tail, Tail?

Step 1: Find the probability of one event.

Step 2: Find the probability of the other event.
The probability of getting Tail, Tail - P(TT) - is:

Step 3: Add the probabilities together, and simplify if necessary.

# Another Real Example of How to Use 'Or' Rule of Probability from a Tree Diagram

Some questions will require more thought as to what outcomes need to be considered, rather than having them spelt out.

The slider below gives a real example of how to use the 'or; rule of probability from a tree diagram.
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##### Note
WHAT IS PROBABILITY?

Probability tells us how likely something is to happen.

The probability of an event is defined as:

Probability is given as a number between 0 and 1.

A probability of 0 means an event is impossible.

A probability of 1 means an event is certain.

The closer a probability is to 0 the less likely it is. The closer a probability is to 1 the more likely it is.

WHAT IS A TREE DIAGRAM?

A tree diagram displays the possible outcomes from an event, and allows the probabilities of different outcomes to be calculated.

# SIZE OF TREE DIAGRAMS

Tree diagrams can be any size.

It would be possible to draw a tree diagram for three coin tosses:

# A USEFUL CHECK

There is a useful way to check that the probabilities on a tree diagram are all right.

Firstly, notice that at each branch, the probabilities add up to 1:

Secondly, when the probabilities of each final outcome are known, they also add up to 1: