Probability Flashcards
How can we define probability?
Weiss definition:
The ratio of the number of time and event occurs in a set of all possible occurrences and the number of all possible occurrences in the full set
Textbook:
We can define probability as the extent to which an event is likely to occur - measured by the ratio of the favorable cases to the whole number of possible cases.
What concept does probability measure?
uncertainty
What possible range of values can a probability have?
A probability can take any value between 0 and 1, where zero is that the event will not occur and 1 the event will certainly occur.
It cannot assume any value lower than zero and greater than one because it is a proportion or percentage whose value cannot exceed 1/1 or 100%
Trial
an action which results in one of several possible outcomes
i.e. rolling a die
Experiment
is a series of trials (or possibly just one)
i.e. rolling one die or multiple dice in succession
Event
is a set of outcomes with something in common
Basic probability formula
P(A) = nA/n
nA = number of times we see A occur n = total possible outcomes
What is the relative frequency of probability?
If, in a large number of independent trials (n), nA of these trials will result in event A.
The idea is that they must be independent
they must be a large number of trials
and there more trials, the closer the probability gets to a constant value
What is subjective probability?
It is the rule of subjective probability that is based in belief, mood, and personality but also can take inot account experimental data from past events
What are the probabilities of compound events?
There is intersection of events such as
P(A and B)
and there is also union of events
P(A or B or both)
How do we calculate P(A and B) using conditional probability and the multiplication law?
We use the multiplication law
P(A and B) = P(A)*P(A|B)
where P(A|B) is the probability that Event 2 will occur given that Event A has already occurred.
What is addition law and when do we use it?
This is the “or” law in which you add the probability of event A and event B. Then you have to subtract the probability of event A and B.
P(A or B or Both) = P(A) + P(B) - P(A and B)
What is mutually exclusive/exhaustive events?
What is it equation?
If all possible outcomes of an experiment are formed into a set of mutually exclusive or exhaustive set, the sum of the probabilities is 1.
E1 + E2 + E3…+ En = 1
What is a complementary event?
What is its equation
For an Event A, there is a complementary Ac, called not A.
1-Ac = A
or
A + Ac = 1.
Law of large numbers
In any experiment, the relative frequency for an event will change from trial to trial. If an experiment is conducted a number if times, the relative frequency of the event will tend to converge toward a number called the probability of the event.
