Two Way Conditional Probability

Front

What is conditional probability?

Back

Conditional probability is the probability of an event occurring given that another event has already occurred.

Front

How is conditional probability mathematically represented?

Back

Conditional probability is represented as P(A|B), which is the probability of event A occurring given that event B has occurred.

Front

What is the formula for calculating conditional probability?

Back

The formula is P(A|B) = P(A and B) / P(B), where P(A and B) is the probability of both events occurring.

Front

What does it mean if two events are independent?

Back

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

Front

How do you determine if two events are independent?

Back

Two events A and B are independent if P(A|B) = P(A) and P(B|A) = P(B).

Front

What is the complement of an event?

Back

The complement of an event A is the event that A does not occur, denoted as A' or not A.

Front

What is the probability of the complement of an event?

Back

The probability of the complement of an event A is given by P(A') = 1 - P(A).

Front

What is the law of total probability?

Back

The law of total probability states that if B1, B2, ..., Bn are mutually exclusive events that cover the entire sample space, then P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn).

Front

What is Bayes' theorem?

Back

Bayes' theorem relates the conditional and marginal probabilities of random events, expressed as P(A|B) = [P(B|A)P(A)] / P(B).

Front

What is the significance of the joint probability?

Back

Joint probability refers to the probability of two events occurring simultaneously, denoted as P(A and B).