Statistics Test #2

Outcome

result of a single trial

Conditional Probability

the probability of an event occurring, given another event HAS AREADY happened. (Given that)

Sample Space

the set of all possible outcomes of a probability experiment

Mutually Exclusive

- Two events are mutually exclusive if they cannot occur at the same time - If two events are disjoint, then the probability of them both occurring at the same time is 0. - P(A and B) = 0 if two events are mutually exclusive, then the probability of either occurring is the same of the probabilities of each occurring. - If two events are mutually exclusive, they cannot be independent and vice versa. (OR)(ADDITION)

Tree Diagram

1. It is a tree it is all connected. 2. Start with fist event list all possible outcomes. 3. Branch out with second event form each branch with each outcome. 4. Repeat until each event is used.

Fundamental Counting Principle

Each event is chosen form its own group Total = multiply together the # of possibilities for each object (How many ways) or (Combinations)

Discrete Probability Distribution

Must have The probability of each value is between 0 and 1, inclusive the sum of the probabilities is 1 Tables Histograms

The Addition Rule

P(A and B) = P(A) + P(B) - P(A and B) - If events are mutually exclusive use P(A or B) = P(A) + P(B)

Multiplication Rule

P(A and B) = P(A) × P(B/A) (out of and without replacement) P(A and B) = P(A) × P(B)

Empirical Probability

P(E) = Frequency of Event E ÷ Total Frequency - The probability of event E is based on relative frequency. (Events already happened) (if there is a table, record, graph, it's empirical)

Classical Probability

P(E) = Number of Outcomes in Event E ÷ Total Number of outcomes in Sample Space - The probability of event E is the number of outcomes divided by all possible outcomes (is a set #)

Simple Event

an event that consists of a single outcome

Probability

is a branch of mathematics that deals with calculating the likelihood of a given event's occurrence, which is expressed as a number between 1 and 0.

Continuous

is a random value that can take on any of the countless number of values in a line interval, measurement

Discrete

is a random value that is countable number or is finite. Ex: Shoe size

Event

is a subset of the sample space

Random Variable

is a variable whose value is a numerical outcome of a random phenomenon. The possible values of a random variable X are all the values in its sample space, S.

Two way Table

is always dependent

Notation

n = number of times in trial p = P(success) q = P(failure)

Expected Value

of a discrete random Variable is the mean of the random variable (Average)(same as Mean)

Independent

one event DOES NOT have any affect on the probability of there other event P(B/A) = P(B)

Dependent

one event's probability IS affected by another event. P(B/A) ≠ P(B)