# What is the difference between independent events and dependent events?

Then teach the underlying concepts
Don't copy without citing sources
preview
?

#### Explanation

Explain in detail...

#### Explanation:

I want someone to double check my answer

36
Feb 23, 2015

Independent Events The probability of one event happening isn't influenced by the outcome of another.

In mathematical terms

$A , B \text{ events} , P \left(A \cap B\right) = P \left(A\right) \cdot P \left(B\right)$
This reads: Probability of A and B happening is equal to the probability of A happening multiplied by the probability of B happening

An equivalent definition

$P \left(A | B\right) = P \left(A\right)$

This reads: The probability of A given B happened is equal the probability of A

Example:
Event A: Rolling a number larger than four on a die in the first roll Event B: Rolling a 6 on a die on the second roll. These events are independent because one roll of a dice doesn't influence the outcome of another dice roll.

Dependent Events Is the oposite.If the outcome of one event influences the probability of the other they aren't independent

$P \left(A | B\right) \ne P \left(A\right)$

Example:
Event A: Rolling a number larger than four on a die Event B: Rolling a 6 on a die on the same roll. These events are dependent because ,as we are in the same dice roll, the occurrence of event B changes the probability of event A, actually it makes it 1.

Observation:
Pay attention that if you are dealing with more than 2 event, for them to be mutually independent every possible combination of them must be. For example, if we are dealing with 3 events, independence means that:

$P \left(A \cap B \cap C\right) = P \left(A\right) \cdot P \left(B\right) \cdot P \left(C\right)$
$\text{ and } P \left(A \cap B\right) = P \left(A\right) \cdot P \left(B\right) , P \left(B \cap C\right) = P \left(B\right) \cdot P \left(C\right) , P \left(C \cap B\right) = P \left(C\right) \cdot P \left(B\right)$

• 7 minutes ago
• 7 minutes ago
• 7 minutes ago
• 9 minutes ago
• 22 seconds ago
• 57 seconds ago
• 58 seconds ago
• A minute ago
• A minute ago
• 2 minutes ago
• 7 minutes ago
• 7 minutes ago
• 7 minutes ago
• 9 minutes ago