Difference Between Independent Events and Dependent Events
The difference between independent events and dependent events is discussed in the table below,
Independent Events |
Dependent Events |
---|---|
Independent events are events that are not affected by the occurrence of other events. |
Dependent events are events that are affected by the occurrence of other events. |
The formula for the Independent Events is, P(A and B) = P(A)×P(B) |
The formula for the Dependent Events is, P(B and A) = P(A)×P(B after A) |
Examples of Independent Events are,
|
Examples of Dependent Events are,
|
Mutually Exclusive Events
Two events A and B are said to be mutually exclusive events if they cannot occur at the same time. Mutually exclusive events never have an outcome in common. If we take two events A and B as mutually exclusive events where the probability of event A is P(A) and the probability of event B is P(B) then the probability of happening both events together is,
P(A∩B) = 0
Then the probability of occurring any one event is,
P(AUB) = P(A) or P(B) = P(A) + P(B)
Dependent and Independent Events
Dependent and Independent Events are the types of events that occur in probability. Suppose we have two events say Event A and Event B then if Event A and Event B are dependent events then the occurrence of one event is dependent on the occurrence of other events if they are independent events then the occurrence of one event does not affect the probability of other events.
We can learn about dependent and independent events with the help of examples such as the event of tossing two coins simultaneously the outcome of one coin does not affect the outcome of another coin then they are independent events. Suppose we take other experiments where we toss a coin only when we get a six in the throw of dice, where the outcome of one event is affected by other events then they are dependent events.
In this article, we will learn about dependent events, independent events, their formulas, examples, and others in detail.
Table of Content
- Dependent and Independent Events in Probability
- Dependent Events
- Examples of Dependent Events
- Independent Events
- Examples of Independent Events
- Difference Between Independent Events and Dependent Events
- Mutually Exclusive Events
- Conditional Probability Formula