# The 'Or' Rule of Probability (Mathematics Lesson)

# What Is the 'Or' Rule of Probability?

Probability tells us how likely something is to happen.It can be used to find out how likely it is to roll a 6 on a die:

Or how likely it is to pick a Club from a deck of cards:

But we might be interested in finding out the probability that either one event

**or**another event occur.

For example,

- What is the probability of rolling a 1
**or**a 6 on a die? - What is the probability of picking a Club
**or**a Spade from a deck of cards?

# How to Use the 'Or' Rule of Probability

For two mutually exclusive events,**A**and

**B**, the probability of

**A or B**occuring is given by adding the probability of

**A**occuring with the probability of

**B**occuring:

# A Real Example of How to Use the 'Or' Rule of Probability

**Question:**What is the probability of rolling a 1 or a 6 on a die?

**Step 1:**Find the probability of one event.

The probability of rolling a 1, P(1), is:

**Step 2:**Find the probability of the other event.

The probability of rolling a 6, P(6), is:

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

The probability of rolling a 1 or a 6 is ⅓.

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

The tree diagram below represents a rolling of a die.Find the branches that represent rolling a 1 and rolling a 6, and add the probabilities together:

This confirms that the probability of rolling a 1 or a 6 is ⅓.

# Another Real Example of How to Use the 'Or' Rule of Probability

The slider below gives a real example of how to use the 'or' rule to find the probability that either of two mutually exclusive events occur.##### Interactive Test

**show**

# THIS APPLIES ONLY TO MUTUALLY EXCLUSIVE EVENTS

The formula shown:P(A

**or**B) = P(A) + P(B)

applies only to

**mutually exclusive**events!

##### Top Tip

**PROBABILITY OF 'OR' = +**

For mutually exclusive events, A and B,

P(A

**or**B) = P(A) + P(B)

**or**= +

##### Note

# ADDING FRACTIONS

As probabilities are often written as fractions, adding them involves adding fractions.**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. The probability of pigs flying is 0 (unless they are put in an aeroplane!).

A probability of 1 means an event is certain. The probability that an elephant is heavier than a fly is 1.

A probability of ½, such as getting a Heads in a coin toss, means it is equally likely to go either way. A coin is as likely to come up Heads as it is to come up Tails.

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 MUTUALLY EXCLUSIVE EVENT?**

Two events are mutually exclusive if they cannot occur at the same time.

If I toss a coin, it cannot land on both Heads and Tails at the same time. Getting a Heads and getting a Tails in a coin toss are mutually exclusive events.

Similarly, if I roll a die, I cannot roll a 1 and a 6 at the same time. Rolling a 1 and rolling a 6 are mutually exclusive events.