# What Is an Independent Event? (Mathematics Lesson)

# What Is an Independent Event?

In probability, two events are independent if the probability of one event occuring does not depend on whether the other event occurs.# Real Examples of an Independent Event

Imagine tossing a coin. The probability of the coin coming up Heads is:If I toss the coin a 2

^{nd}time, the probability of getting a Heads is:

The probability of getting a Head (or a Tail) is the same each time, it doesn't depend on previous tosses. Each toss is independent of the others.

Similarly, if I roll a pair of dice. The probability that I roll a particular number

*this time*does not depend on the number I rolled

*last time*. Each roll is independent of the others.

# Visualizing Independent Events on a Tree Diagram

A tree diagram can be used to illustrate independent events.The tree diagram below illustrates someone tossing a coin twice, once after the other. At each branch, the coin can either be

**H**eads (

**H**) or

**T**ails (

**T**). The

**½**by each branch shows that there is a probability of a ½ each time.

The left-most branch shows the result of the 1

^{st}toss, and the right-most branches shows the results of the 2

^{nd}toss:

The fact that the probabilities are the same in the 1

^{st}and the 2

^{nd}toss shows that each toss is an independent event.

##### Interactive Test

**show**

##### Note

**WHAT IS PROBABILITY?**

Probability tells us how likely something is to happen. 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.

# DEPENDENT EVENTS

The opposite to independent events are**dependent**events.

In this case, each trial depends on what happened before.

An example might be picking a colored marble from a bag without replacing it. Each time a marble is picked out, there will be one less marble in the bag than last time, so there will be a different probability.