Probability: The study of randomness and uncertainty
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.
B:The set containing all outcomes that are in A OR in B OR in both.
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:
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).
|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.