Probability Statements (with Conditionals)

Front

What is a conditional probability?

Back

A conditional probability is the probability of an event occurring given that another event has already occurred, denoted as P(A|B).

Front

What does P(A|B) represent?

Back

P(A|B) represents the probability of event A occurring given that event B has occurred.

Front

What is the formula for conditional probability?

Back

The formula for conditional probability is P(A|B) = P(A and B) / P(B), provided P(B) > 0.

Front

What is the difference between P(A|B) and P(B|A)?

Back

P(A|B) is the probability of A given B, while P(B|A) is the probability of B given A; they are not generally equal.

Front

What is the law of total probability?

Back

The law of total probability states that if B1, B2, ..., Bn are disjoint events that cover the sample space, then P(A) = Σ P(A|Bi)P(Bi).

Front

What is Bayes' theorem?

Back

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

Front

How do you calculate the probability of an event?

Back

The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes.

Front

What is the complement of an event?

Back

The complement of an event A, denoted A', is the event that A does not occur, and P(A') = 1 - P(A).

Front

What is a joint probability?

Back

Joint probability is the probability of two events A and B occurring together, denoted as P(A and B).

Front

What is the difference between independent and dependent events?

Back

Independent events do not affect each other's probabilities, while dependent events do.