Conditional Probability

Front

What is Conditional Probability?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

How is Conditional Probability calculated?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What does P(A|B) represent?

Back

It 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

If P(A) = 0.5 and P(B) = 0.4, and P(A and B) = 0.2, what is P(A|B)?

Back

P(A|B) = P(A and B) / P(B) = 0.2 / 0.4 = 0.5.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the Law of Total Probability?

Back

It states that the total probability of an event can be found by considering all possible ways that event can occur, often using conditional probabilities.

Front

What is the formula for Bayes' Theorem?

Back

P(A|B) = [P(B|A) * P(A)] / P(B), which allows us to update the probability of A based on new evidence 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.

Tags

CCSS.HSS.CP.A.5

Front

If two events A and B are independent, what is P(A and B)?

Back

P(A and B) = P(A) * P(B).

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

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. P(A') = 1 - P(A).

Tags

CCSS.HSS.CP.A.1

Front

What is a joint probability?

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5