Conditional Probability

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 it mean if two events are independent?

Back

Two events A and B are independent if the occurrence of one does not affect the probability of the other. Mathematically, this is expressed as P(A|B) = P(A) or P(B|A) = P(B).

Tags

CCSS.HSS.CP.A.3

Front

What is the formula for the probability of the union of two events?

Back

The probability of the union of two events A and B is given by: P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Tags

CCSS.HSS.CP.B.7

Front

What is the complement of an event?

Back

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

Tags

CCSS.HSS.CP.A.1

Front

How do you find the probability of an event not occurring?

Back

The probability of an event A not occurring is found using the formula: P(A') = 1 - P(A).

Tags

CCSS.7.SP.C.5

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 the Law of Total Probability?

Back

The Law of Total Probability states that if B1, B2, ..., Bn are disjoint events that cover the entire sample space, then for any event A: P(A) = Σ P(A|Bi) * P(Bi).

Front

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

Back

P(A|B) is the probability of A occurring given that B has occurred, while P(B|A) is the probability of B occurring given that A has occurred. They are not generally equal.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is a joint probability?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5