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How to Use the 'Or' Rule for Probability from a Tree Diagram (Mathematics Lesson)

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.
The probability of getting Head, Head - P(HH) - is:



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.



The probability of getting Head, Head or Tail, Tail is ½.

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.
Interactive Test
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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:



Top Tip

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: