Math 333/333H
Week 2
Probability: The study of randomness and uncertainty
Relation between Probability and Statistics
Probability: Assumes properties of population are known and uses
mathematics to answer questions about what we expect to see in a
sample of observations drawn from that population
Statistics: Uses sample of observations to draw conclusions
about the population from which the sample was take
Experiment: An action or process that generates observations.
The sample space is the set of all possible outcomes of an experiment. An event
is a collection of outcomes contained in the sample space. A simple event contains
a single outcome.
Use set theory to study relationships among events.
A
B: The
set containing all outcomes that are in A OR in B OR in both.
A 
B: The set containing
all outcomes that are in A AND in B
A': The
set containing all outcomes that are NOT in A
S: Denotes the set
containing all possible outcomes of an event.
: The empty set, containing no outcomes (the
complement of S, S ' )
Two sets that contain no outcomes in common are mutually exclusive
or disjoint
A probability is a
rule assigning a numerical value to the outcome of an event.
Probability measures must obey the
following rules:
- Probability of an
event, A, must be greater than or equal to zero.
- P(S)=1
- If we have a
collection of mutually exclusive events, the probability of their union is equal to the
sum of their individual probabilities.
The probability of an event, A, can be interpreted as the
proportion of times that event A would occur if the same experiment was carried out
over and over again. (limiting relative frequency).
Properties of Probability
1. P(A') = 1- P(A)
|
2. If A and B are mutually
exclusive, |
 . |
| 3. Additive law of probability: |
 |
If any simple event in an experiment is equally likely, then a
reasonable assignment of probabilities is to let the probability of a simple event
be 1/N, where N is the total number of simple events.