# Dependent Events in Math: Definition & Examples

Instructor: Karin Gonzalez

Karin has taught middle and high school Health and has a master's degree in social work.

In this lesson, we will review the definition of a dependent even in math and the concept and formula for conditional probability. We will also look at some examples to clarify your understanding of this concept.

## Definition of Dependent Event in Math

To help us understand the definition of a dependent event, let us look at a fun example using gummy bears. Who doesn't love gummy bears? If you were blindfolded and asked to pick one gummy bear from a bag of 20 gummy bears, what would be the probability that you would choose a red gummy bear if the bag contained 4 red gummy bears, 5 orange gummy bears, 6 green gummy bears and 5 yellow gummy bears?

In order to find the probability, we would take the number of red gummy bears and put it over the number of total gummy bears. 4/20= 1/5 which is equal to 20%. So, you would have a 20% chance of picking a red gummy bear if you were to reach in and pick one blindfolded.

Now let us imagine that your friend was also blindfolded and asked to pick a gummy bear blindfolded after you picked yours. Would the probability of him picking a red gummy bear be the same as the probability was for you to pick a red gummy bear? No! Why? Because you already picked one, making the total amount of gummy bears in the bag 19 instead of 20.

We would call the event of your friend choosing a gummy bear the dependent event because the outcome of you choosing a gummy bear affects the outcome and probability of your friend choosing a gummy bear.

So, a dependent event in math is one in which the outcome and probability are affected by a preceding event.

## Conditional Probability

If we want to find the probability of a dependent event occurring, it is called conditional probability. Conditional probability is the probability of Event B occurring given that Event A occurred.

Remember the bag of 20 gummy bears? You picked from the bag (Event A) and picked a red gummy bear. The dependent event was your friend picking from the bag next (Event B). The conditional probability of the dependent event (Event B) is determined by what happened in Event A. Let's look at how, exactly.

The conditional probability of your friend picking a red gummy bear given that you picked a red gummy bear would be 3/19 because there are only 3 red gummy bears left in the bag of 19 total gummy bears.

The conditional probability of your friend picking a red gummy bear given that you did not pick a red gummy bear would be 4/19 because there are still 4 red gummy bears left in the bag of 19 total gummy bears.

## Finding the Probability of Both Events Occurring

What if we want to find the probability of both Event A (you picking a red gummy) and Event B (your friend picking a red gummy too) occurring? We would multiply them!

Event A (you picking red gummy bear) probability= 1/5

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