Conditional Probability and the Multiplication Rule

Flashcards covering key concepts from Conditional Probability and the Multiplication Rule lecture notes.

Conditional Probability

The probability of an event occurring, given that another event has already occurred, represented as P(A|B).

Multiplication Rule

A formula used to find the probability of the intersection of two events, P(A and B) = P(A) × P(B|A) for dependent events.

Independence

Two events are independent if the occurrence of one event does not change the probability of the other event.

Probability of A occurring given B has occurred

P(A|B) is the notation used for conditional probability.

P(Failed Chem and Failed Bio)

The probability that a student fails both Chemistry and Biology, given as 0.06 in the lecture notes.

False Positive

A test result that indicates a person has a disease when they actually do not.

False Negative

A test result that indicates a person does not have a disease when they actually do.

Tree Diagram

A graphical representation used to visualize the possible outcomes of a sequence of events.

P(H|A)

The probability of event H occurring given that event A has occurred.

Venn Diagram

A diagram that shows all possible logical relations between different sets, used to illustrate probabilities in this context.

P(Someone who tests positive has the disease)

The probability that a person who tests positive actually has the disease, calculated using conditional probability.

Admitted = .5395

The probability of being admitted to a top school given high GPA/SAT scores.

P(Have|Test neg)

The conditional probability of having a disease given a negative test result.

GPA/SAT

Grade Point Average and Scholastic Aptitude Test scores, often used as indicators for college admissions.

P(Participates | Female)

The probability of participating in after-school sports given that the student is female.

Dependency

When the probability of one event is influenced by the occurrence of another event.