STOR 151
Copyright © Wonyul Lee
1
4.5 Conditional Probability and Independence
Exercise 4.48
In a class of 32 seniors and graduate students, 20 are men and 12 are graduate students
of whom 8 are women.
Senior Graduate Student Total
Male 20
Female 8
Total 12 32
• Suppose a student is randomly selected from this class
• Event A = the student is a graduate student
• Event B = the student is male
• Event AB=
• P(A)=
• P(B)=
• P(AB)= P(A B) =
• Question: Does the probability of event A change when it is known that event B has
occurred?
• That is, what’s the probability of the selected student is a graduate student given that the
student is male?
Conditional Probability
• Conditional probability of A given B: The revised probability of an event A when it is
known that B has occurred.
• Notation: P(A|B)
• Previous example:
Formula for conditional probability
• P(A|B)=P(AB)/P(B); P(B|A)=P(AB)/P(A)
• Alternative forms: P(AB)=P(B)P(A|B) and P(AB)=P(A)P(B|A) are called the multiplication
laws of probability.
• Previous example:
