Chapter 3: Probability Topic

is a planned operation carried out under the controlled condition

Result of an experiment

a set of all possible outcomes

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

Each outcome of an experiment has the same probability.

the chance of the outcome of an 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.

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

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

A given B is written P(A|B’)

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

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

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.

P(A|B) = P(A)

P(B|A) = P(B)

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

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

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

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

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

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

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.