Conditional Probability

1. Conditional Probability : Given that an event (with non-zero probability) has occurred, the probability that event occurs is called the conditional probability of event given event , denoted as .
2. The conditional probability of event given that event has occurred is:
3. For two events and where , , and ,
   

[Explanation] and represent the probabilities of events and occurring in the entire sample space .
However, conditional probability considers a reduced sample space, where is the new sample space. Thus, means the probability of event occurring, assuming that has already occurred.

Proportion of in the entire space	Proportion of in the entire space	Proportion of within

 

Example 1. For two events and

Given, find the value of(Noteand are coprime natural numbers)

 Solution

Answer :

 

Example 2. For two events , we have

Find the value ofin(Note thatand are coprime natural numbers)

 Solution

에서

At

Answer :