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

How is Conditional Probability calculated?

Back

P(A|B) = P(A and B) / P(B), where P(A|B) is the probability of A given B.

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 Bayes' Theorem?

Back

P(A|B) = [P(B|A) * P(A)] / P(B) where P(B) is the total probability of B.

Front

If P(A) = 0.4 and P(B) = 0.5, what is P(A and B) if A and B are independent?

Back

P(A and B) = P(A) * P(B) = 0.4 * 0.5 = 0.2.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the complement of an event?

Back

The probability that the event does not occur, calculated as 1 - P(A).

Tags

CCSS.HSS.CP.A.1

Front

What is the Law of Total Probability?

Back

If B1, B2, ..., Bn are disjoint 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 an example of Conditional Probability in real life?

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

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

How do you interpret P(A|B) = 0.3?

Back

There is a 30% chance that event A occurs given that event B has occurred.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5