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 means 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 and B) / P(B), where P(A and B) is the probability of both events 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 formula states that P(A) = P(A|B)P(B) + P(A|not B)P(not B).

Front

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

Back

If A and B are independent, P(A and B) = P(A) * P(B) = 0.5 * 0.4 = 0.2.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

Front

What is the Complement Rule in probability?

Back

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

Tags

CCSS.HSS.CP.B.7

Front

What is the difference between independent and dependent events?

Back

Independent events are those whose outcomes do not affect each other, while dependent events are those where the outcome of one event affects the outcome of another.

Tags

CCSS.HSS.CP.A.5

Front

How do you find P(A|B) when given a contingency table?

Back

To find P(A|B) from a contingency table, divide the number of occurrences of A and B by the total occurrences of B.

Tags

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 an example of Conditional Probability in real life?

Back

An example of Conditional Probability is determining the probability of a person being a smoker given that they have lung cancer.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5