DEPENDENT EVENTS

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. 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.

Real-world Connections for Dependent Events

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

Quick Summary

Dependent events are events where the outcome of one affects the outcome of another.
Not replacing items after selection leads to dependent events.
Conditional probability is used to calculate probabilities of dependent events.

\[ P(A \cap B) = P(A) \cdot P(B|A) \]

🍎 Teacher Insights

Use real-world examples and simulations to illustrate dependent events. Emphasize the importance of adjusting probabilities in conditional probability calculations.

🎓 Prerequisites

Basic Probability
Independent Events
Conditional Probability

Check Your Knowledge

Q1: Which of the following is an example of dependent events?

A. Flipping a coin twice. B. Rolling a die and spinning a spinner. C. Drawing a card from a deck and not replacing it, then drawing another card. D. All of the above.

Q2: If event A affects the probability of event B, then A and B are:

A. Independent B. Mutually Exclusive C. Dependent D. Complementary

Frequently Asked Questions

Q: How do I identify dependent events?
A: Check if the outcome of the first event changes the probabilities of subsequent events. If it does, they are dependent.

Q: What is the difference between dependent and independent events?
A: Independent events do not affect each other's outcomes, while dependent events do.