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

What is the formula for conditional probability?

Back

The formula for conditional probability is P(A|B) = P(A ∩ B) / P(B), where P(A|B) is the probability of A given B.

Front

What does the intersection of two events represent?

Back

The intersection of two events represents the outcomes that are common to both events, often denoted as A ∩ B.

Front

What are independent events?

Back

Independent events are events where the occurrence of one event does not affect the occurrence of another event.

Front

How is the complement of an event denoted?

Back

The complement of an event A is denoted as 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

If two events are mutually exclusive, what does that mean?

Back

Mutually exclusive events cannot occur at the same time; the occurrence of one event means the other cannot occur.

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) = Σ P(A|Bi)P(Bi).

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 difference between joint probability and conditional probability?

Back

Joint probability refers to the probability of two events occurring together, while conditional probability refers to the probability of one event occurring given that another event has occurred.