Difference Between Independent and Dependent Events
The key distinction between independent and dependent events lies in how the outcome of one event affects the probability of another. In the following table all the major differences between both dependent and independent events are given:
| Aspect | Dependent Events | Independent Events |
|---|---|---|
| Definition | Events where the outcome of one event affects the outcome of another. | Events where the outcome of one event does not affect the outcome of another. |
| Dependency | The occurrence of one event influences the probability of the other event. | The occurrence of one event has no influence on the probability of the other event. |
| Sampling | Often occurs when sampling without replacement. | Typically occurs when sampling with replacement. |
| Conditional Probability | Conditional probability differs from marginal probability. | Conditional probability equals marginal probability. |
| Example | Drawing cards from a deck without replacement. | Flipping a coin and rolling a die simultaneously. |
| Formula | P(A∩B) = P(A) × P(B∣A) | P(A∩B) = P(A) × P(B) |
Dependent Events
Dependent Events in Probability: Dependent events are those events that are affected by the outcomes of events that had already occurred previously. i.e. Two or more events that depend on one another are known as dependent events. If one event is by chance changed, then another is likely to differ.
In this article, we will discuss Dependent Events in detail, including their examples, theorem, as well as the method to calculate the probability of dependent events, and the difference between Dependent Events and Independent Events.
Table of Content
- What are Events in Probability?
- What are Dependent Events in Probability?
- Dependent Events Definition
- Dependent Events Examples
- Probability of Dependent Events
- Dependent Events Formula
- Difference Between Independent and Dependent Events
- Dependent Events: Examples in Real Life
- Dependent Events – Solved Examples
- Practice Problems on Dependent Events
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