Chapter 3: Probability Topic

Experiment

is a planned operation carried out under the controlled condition

Outcome

Result of an experiment

Sample space

a set of all possible outcomes

Event

any combination of outcomes that are usually represented by the letters A and B.

Equally Likely

Each outcome of an experiment has the same probability.

Probability

the chance of the outcome of an event

“OR” Event

an outcome is in the event A OR B if the outcome is in A or is in B or is in both A and B.

"AND" Event

an outcome is in the event A AND B if the outcome is in both A and B at the same time.

Conditional probability

A given B is written P(A|B). P(A|B) is the probability that event A will occur given that event B has already occurred

Complement

A given B is written P(A|B’)

Independent

One event occurring does not affect the chance that the other event occurs.

Sampling with replacement

then events are considered to be independent, meaning the result of the first pick will not change the probabilities for the second pick.

Sampling without replacement

the probabilities for the second pick are affected by the result of the first pick. The events are considered to be dependent or not independent.

The events are independent if this is true

P(A|B) = P(A)

P(B|A) = P(B)

P(A AND B) = P(A)P(B)

Mutually exclusive

If events occur at the same time -> P(A and B) = 0

Multiplication Rule

If A and B are two events defined on a sample space, then

Addition Rule

If A and B are defined on a sample space, then

Contingency table

provides a way of portraying data that can facilitate calculating probabilities.

Tree diagrams

used to determine the outcomes of an experiment. It consists of "branches" that are labeled with either frequencies or probabilities.

Venn diagrams

a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.