Conditional Probability Practice

Front

What is Conditional Probability?

Back

Conditional Probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads as 'the probability of A given B'.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

How is Conditional Probability calculated?

Back

Conditional Probability is calculated using the formula: P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B occurring.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What does P(A|B) represent?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the formula for Total Probability?

Back

The Total Probability theorem 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 the Complement Rule in probability?

Back

The Complement Rule states that the probability of an event not occurring is equal to 1 minus the probability of the event occurring: P(A') = 1 - P(A).

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the difference between independent and dependent events?

Back

Independent events are those whose occurrence does not affect the probability of another event occurring. Dependent events are those where the occurrence of one event affects the probability of another event.

Tags

CCSS.HSS.CP.A.5

Front

How do you determine if two events are independent?

Back

Two events A and B are independent if P(A ∩ B) = P(A) * P(B). If this equality holds, the events are independent.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is Bayes' Theorem?

Back

Bayes' Theorem relates the conditional and marginal probabilities of random events. It is expressed as: P(A|B) = [P(B|A) * P(A)] / P(B).

Front

What is a joint probability?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is a marginal probability?

Back

Marginal probability is the probability of an event occurring without consideration of any other events. It is denoted as P(A) or P(B).