Mathematics for Computer Science
MIT 6.042J/18.062J
Probability
Spaces
Albert R Meyer,
May 1, 2012
samplespace.1
Probability Spaces
1) Sample space: a countable
set  whose elements are
called outcomes
2) Probability function,
Pr: [0, 1], such that
Albert R Meyer,
May 1, 2012
samplespace.2
Probability Spaces
The purpose of the “tree
model” is to figure out which
probability space to use:
• outcomes = leaves of tree
• outcome probabilities
calculated from branch
probabilities.
Albert R Meyer,
May 1, 2012
samplespace.3
Probability Spaces
An event is a subset, E 
S.
Cor: The Sum Rule
Albert R Meyer,
May 1, 2012
samplespace.4
Sum Rule
For pairwise disjoint A0,A1,…
Pr[A 0 È A1 È A2 È ] =
Pr[A 0 ] + Pr[A1 ] + Pr[A2 ] +
Albert R Meyer,
May 1, 2012
samplespace.5
Sum Rule
For pairwise disjoint A0,A1,…
Albert R Meyer,
May 1, 2012
samplespace.6
Discrete Probability
Discrete = countable
sample space
Allows sums instead
of integrals
Albert R Meyer,
May 1, 2012
samplespace.7