**Definition of Dependent Events**

- If the outcome of one event affects the outcome of another, then the events are said to be Dependent Events.

**Examples of Dependent Events**

- Taking out a marble from a bag containing some marbles and not replacing it, and then taking out a second marble are dependent events.

**Solved Example on Dependent Events **

Which of the following are dependent events?

1. Getting an even number in the first roll of a number cube and getting an even number in the second roll.

2. Getting an odd number on the number cube and spinning blue color on the spinner.

3. Getting a face card in the first draw from a deck of playing cards and getting a face card in the second draw. (The first card is not replaced.)

Choices:

A. 2

B. 2 and 3

C. 1 and 3

D. 3

Correct Answer: D

Solution:

Step 1:In (1), rolling a number cube two times are two independent events.

Step 2:In (2), rolling an odd number and spinning blue color are two independent events.

Step 3:In (3), since the first card is not replaced back, the probability of the second draw depends on the first draw.

Step 4:So, the two events in (3) are dependent events.

**Related Terms for Dependent Events**

- Event
- Outcome

**Real-world Connections for Dependent Events **

- If we wake up late, we will be late to office.
- If it rains, we use an umbrella.