Conditional Probability

Front

What is Conditional Probability?

Back

The probability of an event occurring given that another event has already occurred.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What does P(A|B) represent?

Back

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 Conditional Probability?

Back

P(A|B) = P(A and B) / P(B), provided P(B) > 0.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What are Independent Events?

Back

Two events A and B are independent if the occurrence of one does not affect the occurrence of the other.

Tags

CCSS.HSS.CP.A.5

Front

How do you determine if two events are independent?

Back

Check if P(A|B) = P(A) or P(B|A) = P(B). If true, they are independent.

Tags

CCSS.HSS.CP.A.3

Front

What is the Complement Rule in probability?

Back

The probability of an event not occurring is 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 Total Probability Theorem?

Back

If B1, B2, ..., Bn are mutually exclusive events that cover the sample space, then P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn).

Front

What is Bayes' Theorem?

Back

A way to find a conditional probability when you know the reverse conditional probability: P(A|B) = [P(B|A) * P(A)] / P(B).

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.

Front

What is an example of Conditional Probability?

Back

The probability of a student passing a test given that they studied for it.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5