Discrete Mathematics CS 2610. November 5, 2008. Probability Theory. When dealing with experiments for which there are multiple outcomes- x 1 , x 2 , …, x n –we require 0 p( x i ) 1 for i = 1, 2, …, n and (i=1, n) p( x i ) = 1
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November 5, 2008
Uniform Probability Distribution:
p(xi) = 1/n, for i = 1, 2, …, n
All outcomes are equally probable.
Note that sum and product rules apply when dealing with probabilities too!
Sequences of events are products
Either/or requires sum rule and subtraction principle
Complementary rule works too!
The conditional probability of E given F is
P(E | F) = p(E F) / p(F)
This is the probability that E will/has occurred if we know that F has/will occur.
Two events, E and F, are independent iff
p(E1 E2) = p(E1) p(E2)
The two events don’t influence one another!
If there are a number of trials being conducted, each of which has a probability of success of p and a probability of failure of q = 1 – p, then the probability of exactly k successes in n independent trials is
This is called the binomial distribution.