Chapter 3: Probability Theory Flashcards
Probability Theory is a branch of
A branch of Mathematics concerned with the analysis of random phenomena.
It gives you the tools to describe things around you that are random.
Experiment
any repeatable process from which an outcome, result or measurement is obtained.
Random Experiment
an experiment that produces a definite outcome that cannot be predicted with certainty
Trial
one repetition of a Random Experiment
Sample Space
set of all possible outcomes based on a random experiment
- Event
2. An Event (E) is said to occur…
subset of a sample space: any set of outcomes. An event (E) is said to occur on a particular trial of the experiment if the outcome observed is an element of the set (E).
Simple Element
any basic outcome from a random experiment
composite element
any combo of 2 or more basic outcomes from a random experiment.
Probability of an outcome (e) in the sample space (s)
a number p between 0 and 1 that measures the likelihood that (e) will occur in a single trial of a random experiment.
Probability of an event (A) denoted by P(A)
is the sum of all the probabilities of the individual outcomes of which it is composed.
Permutation
a permutation of n different things taken x at a time is an arrangement in a specific order of any x of n things
combination
a combination of n things taken x at a time is an arrangement of any x of these things in no particular order.
A ∩ B (and)
collection of all outcomes that are elements of the sets A and B
Mutually Exclusive: P(A∩B)=0
Events A and B are mutually exclusive or disjoint if they have no elements in common.
Impossible for A and B to occur simultaneously.
A U B (or)
collection of all outcomes of both A and B, or one of them.
Additive Rule
P(AUB) = P(A)+P(B)-P(A∩B)
Special Addition Law
For any 2 mutually exclusive events:
P(AUB)=P(A)+P(B)
Complements
The complement of an event are all elements in the sample set that are not a part of the event.
P(A’) = 1 - P(A)
Unconditional Probability
The likelihood that a particular event will occur, regardless of whether or not another event occurs
Conditional Probability
The Probability that an event has occurred in a trial of a random experiment given that another event B has also occurred
p(A|B) = p(A ∩ B) / p(B) .
Joint Probability
the likelihood that 2 events occur at the same time
Collectively exhaustive events
Set of events is collectively exhaustive is the union contains all the basic outcomes of the sample space
A and A’ are collectively exhaustive and mutually exclusive
Partition
events that are collectively exhaustive and mutually exclusive
Joint probability table
Shows frequencies or relative frequencies for joint events
When would you use Baye’s Theorem?
If you have a hypothesis,
You’ve looked at evidence,
You want to find the probability that your hypothesis is true, given that the evidence is also true.
