MATH 3033 based on Dekking et al. A Modern Introduction to Probability and Statistics. 2007 Slides by James Connolly Instructor Longin Jan Latecki . C3: Conditional Probability And Independence. 3.1 – Conditional Probability.
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MATH 3033 based onDekking et al. A Modern Introduction to Probability and Statistics. 2007Slides by James Connolly Instructor Longin Jan Latecki
C3: Conditional Probability And Independence
Provided P(C) > 0
3.2 – Multiplication Rule
For any events A and C:
The Law of Total Probability
Suppose C1, C2, … ,CM are disjoint events such that
C1 U C2 U … U CM = Ω. The probability of an arbitrary
event A can be expressed as:
Suppose the events C1, C2, … CM are disjoint
and C1 U C2 U … U CM = Ω. The conditional probability of Ci, given an arbitrary event A, can be expressed as:
An event A is called independent of B if:
That is to say that A is independent of B if the probability of A occurring is not
changed by whether or not B occurs.
Tests for Independence
To show that A and B are independent we have to prove just one of the following:
A and/or B can both be replaced by their complement.
Independence of Two or More Events
Events A1, A2, …, Am are called independent if:
This statement holds true if any event or events is/are replaced by their
complement throughout the equation.