Math 2200 - Chapter 4
4 Probability Concepts
Definition: Event
Any collection of outcomes in an experiment.
Definition: Sample space
All possible outcomes
Definition: probability of E occurring
If E is an event, f the frequency of that event, and N the total number of possible outcomes, the
probability of E occurring is P(E), where P(E) = f/N.
3 Basic Properties of Probabilities
For any event E,
i. 0£ P(E)£ 1
ii. P(E) = 1 if E is sure to occur (certain event)
iii. P(E) = 0 if E is impossible to occur (impossible event)
Definition: Let A and B be events:
not A means A doesn’t occur
A and B means A and B both occur
A or B means A or B or both occur
Definition: mutually exclusive events
For two events, at most one can occur.
Theorem: Special Addition Rule (OR) - if A and B are mutually exclusive events, then P(A or B) = P(A) + P(B) ({xi} mutually
exclusive events implies P(x1 or x2 or …) = )
Theorem: General Addition Rule (OR) - if A and B are any two events, then P(A or B) = P(A) + P(B) - P(A and B)
Theorem: Complementation Rule - If E is any event, then P(E) = 1 - P(not E)
Definition: contingecy tables
Cross-classifying members of a population or sample according to two variables.
Definition: conditional probability of B given A
Let A and B be two events. The probability that B occurs given that A has occurred the conditional probability of B given A,
written P(B|A).
Theorem: (Conditional Probability Rule) P(B|A) =
Theorem: (Multiplication Rule) - For any two events, A and B, P(A&B) = P(A)P(B|A).
Definition: independence of two events
Two events A and B are independent if the occurrence of A doesn’t affect the probability of the occurrence of B.
(i.e., P(B|A) = P(B) )
Theorem: Special Multiplication Rule - P(A&B&C&...)=P(A)P(B)P(C)…
