Question

What is the difference between independent and conditional probability? give an example of each. Which one requires the use of addition rule?

Answer 1

Independent events have no effect on the occurrence (or non-occurrence) of each other.
Events A and B are independent if, and only if\[\large P(A\cap B)=P(A) \times P(B)\]
Also A and B are independent if
\[\large P(A|B)=P(A)\]
and
\[\large P(B|A)=P(B)\]

Answer 2

Conditional probability is the probability of an event occurring given that another event has already occurred. The conditional probability of A occurring, given that B has occurred, is written P(A|B).
The formula for conditional probability is
\[\large P(A|B)=\frac{P(A\cap B}{P(B)}\]