# How to Identify Independent and Dependent Events?

In this post blog, we will teach you the definition of independent and dependent events and how to identify them.

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**A step-by-step guide to** **independent and dependent events**

There are two types of events in probability, often classified as independent events or dependent events:

**Independent events**:

If the outcome of one event does not affect the outcome of another event, two events are called **independent events**. Or we can say that if one event does not affect the probability of another event, it is called an independent event.

**Independent events formula:**

If two events \(A\) and \(B\) are independent, then the probability of happening of both \(A\) and \(B\) is:

\(\color{blue}{P\left(A\:⋂\:B\right)=P\left(A\right).\:P\left(B\right)}\)

**Dependent events:**

If the outcome of one event affects the outcome of another event, two events are said to be **dependent**. More likely, dependent events are usually actual events that rely on another event to occur.

**Dependent events formula:**

If \(A\) and \(B\) are dependent events, then the probability of \(A\)** **and \(B\) occurring is:

\(\color{blue}{P\left(B\:and\:A\right)=P\left(A\right)×P\:\left(B\:after\:A\right)}\)

**How to identify independent events?**

Before applying probability formulas, an independent or dependent event must be identified. A few steps to check if the probability belongs to a dependent or independent event:

**Step 1:**Check if it is possible for the events to happen in order. If yes, go to step \(2\) or go to step \(3\).**Step 2**: Check if one event affects the outcome of the other event. If yes, go to step \(4\), or else go to step \(3\).**Step 3**: The event is independent. Use the formula of independent events and get the answer.**Step 4:**The event is dependent. Use the formula of the dependent event and get the answer.

**Independent and Dependent Events** **– Example 1:**

A juggler has seven red, five black, and four yellow balls. During the stunt, he accidentally drops a ball and doesn’t pick it up. As he continues, another ball drops. What is the probability that the first ball dropped is yellow and the second ball is black?

**Solution:**

The probability of the first ball is yellow: \(P\) \(=\frac{4}{16}\)

The probability of the second ball is black: \(P\)\(= \frac {5}{15}\)

\(P\left(yellow\:than\:black\right)\:=\:P\left(yellow\right)×\:P\left(black\right)\:\)

\(=\frac{4}{16}× \frac{5}{15}=\frac{1}{12}\)

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