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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
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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.