Conditional Probability

Let A and B be two events. The conditional probability of event A, given that event B has occurred, is denoted by the symbol P(A/B) and is fond to be

Example: A hamburger chain found that 75% of all customers use mustered, 80% use ketchup, and 65% use both. What are the probabilities that ketchup user uses mustard and mustard user uses ketchup? 
Solution: Let A be the event “Customer uses mustard” and B the event “Customer uses ketchup.” Thus, we have

The conditional probability that ketchup user uses mustard is the conditional probability of event A, given B.

In the same way, the probability that a mustard user uses ketchup is

These calculations can also be developed using the following Table.

Table: Joint Probability for Mustard and Ketchup 

	Mustard	No Mustard	Total
Ketchup	0.65	0.45	.080
No Ketchup	0.10	0.10	0.20
Total	0.75	0.25	1.0

Example: Suppose, the residents of a town are classified according to two attributes, the ownership of a house (A) and the ownership of a car (B). The following table summarizes the information:

 Suppose we know that a person chosen at random has a house. What is the probability that he has a car too?

Solution: Here