Module 7, Probability Flashcards
Venn diagram
A type of chart that illustrates how distinct sets, topics, or objects relate to one another. Uses circles to represent events.
complement
An event that is the opposite of another event. The complement of heads when flipping coins is tails. The probabilities of an event and its complement always sum to 1.
Experiement
A procedure that can be done repeatedly which has a well defined set of outcomes.
dependent events
Two events for which the occurrence of the first affects the probability of the second.
relative frequency
A way to approximate a probability by taking the number of times an event occurs divided by the total number of trials.
the law of large numbers
As the number of trials increases the empirical probability converges on the theoretical probability, that is the estimate of the true probability becomes more accurate.
event
An outcome, or set of outcomes, whose chance of occurrence can be represented with a probability.
sample size
The number of different outcomes for an experiment.
tree diagram
A diagram that records all the events in a sample space by attaching each new set of events to each branch of the earlier events. The number of outermost branches gives the sample size.
random experiment
Experiment in which the outcome is not known ahead of time and in which results do not affect future outcomes.
conditional probability
A probability that depends on the occurrence of an earlier event.
law of total probability
A fundamental principle of probability which states that the product of all branches of a probability tree, added together equals 1.
probability
The chance of an event occurring.
independent events
Events, where the occurrence of one does not affect the probability that the other event(s) will occur.
probability tree
A tree diagram in which the branches record the probability of the next event and the nodes record the events.
union
The union of A and B will have all elements in A, all elements in B, and all elements in both. You can think of a union as ‘A or B,’ since it contains an element if it is in A or in B. The union of many sets will have an element if it appears in at least one set.
intersection
The intersection of A and B will have all elements that are in both A and B. You can think of an intersection as ‘A and B,’ since it contains an element if it is in A and in B. The intersection of many sets will have an element if it appears in all of the sets..
frequency table
A table which records the frequency of instances in different categories. It can be used to determine if the categories are dependent or independent.
sample space
The entire set of outcomes for a trial or experiment.
fair
An experiment in which all outcomes are equally likely.
theoretical probability
Also called the Actual, Exact, or Classical Probability, it is computed by dividing the number of outcomes where the desired event occurs by the total number of outcomes. Note that the outcomes must be equally likely.
empirical probability
An estimation of probability derived from recording data about what has happened during a series of experiments.
population
An entire pool from which a sample is drawn.
disjoint
Two events which cannot both occur at the same time.
multiplication rule for independent events
If two events are independent, then P(A and B) = P(A) x P(B).
sample
The small quantity of data gathered about a population that will represent the population as a whole.
