Dependent Events
Definition of Dependent Events
If the outcome of one event affects the outcome of another, then the events are said to be Dependent Events.
More About 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
Video Examples: Dependent Events Conditional Probability
Solved Example on Dependent Events
Ques: 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. 2B. 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.
Realworld Connections for Dependent Events
 If we wake up late, we will be late to office.
 If it rains, we use an umbrella.
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