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31 terms

probability experiment

any process with a result determined by chance

sample space

the set of all possible outcomes of an experiment

event

a subset of a sample space

tree diagram

a kind of diagram with branching that allows outcomes to be organized and counted

subjective probability (personal)

an educated guess regarding an outcome of an experiment, particularly one that can't be (easily) repeated

experimental probability (empirical)

the proportion of outcomes belonging to an event to the total number of experimental trials

classical probability (theoretical)

the proportion of outcomes in an event to the total number of elements in the sample space (if all the events in the sample space are equally likely); a probability determined from knowledge of the world rather than experiment

The Law of Large Numbers

after a large number of experiments, the experimental probability will approximate the classical probability... and will get closer as the number of experiments increases

complement

if E is an event, then this is 1-P(E)

1

the sum all probabilities must add to

0

the probability of an impossible event

1

the probability of a certain event

mutually exclusive

the probability of the intersection of two events is 0//two sets that have no overlap

independent

the two experiments do not effect the outcome of the other

dependent

the two experiments do effect the outcome of each other

conditional probability

the probability of an event after another dependent event has occurred

Fundamental Counting Principle//Multiplication Rule

a rule for calculating elements in a set (sample space or event) for sample spaces illustrated by tree diagrams, or where repeated use of the same outcome in successive experiments is allowed

factorial

multiply all the numbers from n down to 1

combination

a counting rule for when repetition is not allowed, and order doesn't matter

permutation

a counting rule for when repetition is not allowed, but order does matter

special permutations

a counting rule used when order matters and no repetition is allowed, but some elements can't be distinguished from each other

random variable

a variable whose outcome is determine by chance

discrete random variable

a random variable whose outcome can take on only some particular (usually numerical) values

probability distribution

a table or formula that gives the probabilities for every value of a random variable

expected value

the mean of the probability distribution: the expected mean of repeated trials of the experiment

variance of a discrete random variable

a measure of the spread of a discrete probability distribution

binomial distribution

a discrete random variable distribution where trials are fixed in number, independent and have only two outcomes

success

the outcome of interest in a binomial distribution

normal distribution

a continuous probability distribution defined only by its mean and standard deviation

density curve

the curve that defines the probability of a continuous distribution (area under the curve is equivalent to the probability)

continuity correction

the modification to the boundaries of a binomial range when estimating with the normal distribution