Exam 2 review Flashcards
A value between 0 and 1, inclusive, describing the relative possibility an event will occur
Probability
A process that leads to the occurrence of one and only one of several possible results
Experiment
A result of an experiment
Outcome
A collection of one or more outcomes of an experiment
Event
The total arrangements of (m)(n) where m and n are total number of possibilities of events. three dice has 6 outcome for each, so (6)(6)(6) is the formula
Multiplication Fourmula
When there is a single group of events and we want to determine the number of all possible arrangements of an outcome from the group.
An arrangement of r objects selected from a single group of n possible objects
Permutation
An event of outcomes when the order of the outcomes does not matter
Combination
Probability that is based on the assumption that the outcomes of and experiment are equally likely. What is the formula
Classical probability
favorable outcomes/possible outcomes
The occurrence of one event means that none of the other events can occur at the same time.
mutually exclusive
When a list of outcomes is complete (shows all outcomes)
Collectively exhaustive
Law that states over a large number of trials, the empirical probability of an event will approach it’s true probability
law of large numbers
The likelihood of a particular event happening that is assigned by an individual based on whatever information is available
Subjective Probability
Rule that states that if A and B are mutually exclusive the probability of one or the other occurring equals the sum of their probabilities. State rule and formula
Special rule of addition
P(A) + P (B)
Used to compute the probability of two events that are not mutually exclusive
general rule of addition
P(A or B) = P(A) + P(B) - P(A and B)
Rule that state the odds of something happening plus the odds of it not happening must equal 1
complement rule
A probability that measures the likelihood two or more events will happen concurrently
Joint probability
Rule that states if two independent events A and B, the probability that a and b will both occur is found by multiplying the two probabilities
Special rule of multiplication
Used when the conditional probability is required to compute the joint probability of two events that are not independent
General rule of multiplication
P(A and B) = P(A) P(B/A)
The occurrence of one event has no effect on the probability of the occurrence of another event
Independence
The probability of a particular event occurring, given that another event has occurred
conditional probability
A table used to classify sample observations according to two or more identifiable categories or classess
Contingency table
A visual that is helpful in organizing and calculating probabilities for problems similar to the previous example/solution.
tree diagram
Formula used to calculate posterior probability
Bayes Theorem
The initial probability based on the present level of information
Prior probability
A revised probability based on additional information
Posterior probability
A listing of all the outcomes of an experiment and the probability associated with each outcome
probability distribution
A variable measured or observed as the result of an experiment. By chance, the variable can have different values.
Random variable
A discrete distribution where
1. An outcome on each trial is classified as success of failure
2. The random variable is the number of successes
3. The probability of success is the same for each trial
4. The trials are independent
binomial probability distribution
A discrete distribution where
1. An outcome on each trial is a success of failure
2. The random variable is the number of successes
3. The trials are not independent
4. We assume that we sample from a finite population without replacement. The probability changes with each trial
Hypergeometric probability distribution
A discrete distribution where
1. Describes the number of times some event occurs during a specified interval
2. The probability of the event is proportional to the size of the interval
3. The intervals do not overlap
Poisson probability distribution
A continuous probability distribution where the shape is always rectangular with a base determined by the minimum value of a and a height of maximum value of b.
Uniform Probability distribution
A normal probability distribution with a mean equal to 0 and variance equal to 1
Normal probability distribution
This continuous probability distribution usually describes times between events in a sequence.
exponential probability distribution
