Conditional Probability and Bayes's Formula

These flashcards cover key terminologies and concepts related to conditional probability, Bayes's theorem, and independent events as discussed in the lecture notes.

Conditional Probability

The probability that an event E occurs given that another event F has occurred, denoted P(E|F).

Bayes's Formula

A formula used to determine conditional probabilities, expressed as P(A|B) = P(B|A)P(A)/P(B).

Independent Events

Two events E and F are independent if the occurrence of one does not affect the probability of the other, i.e., P(E|F) = P(E).

Intersection of Events

The probability that both event E and event F occur, denoted as P(EF) or P(E and F).

Law of Total Probability

The theorem that relates marginal probabilities to conditional probabilities, allowing calculation of P(B) by considering all possible ways B can occur.

Tree Diagram

A graphical representation of probabilities that shows the different branches of dependent and independent events.

False Positive

A test result which indicates a positive outcome for a condition when it is actually not present.

Probability of Reinfection

The likelihood of an individual testing positive for a condition after recovering from it, often less likely than initial positive tests.

Euler Diagram

A diagram that illustrates the relationships between different sets or events, often used to represent conditional probabilities.

P(E|F)

The notation for the conditional probability of event E given event F has occurred.

P(E)

The notation for the unconditional probability of event E occurring.