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 event A occurring given that event B has occurred.

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 and P(B) is the probability of event B.

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 Law of Total Probability?

Back

The Law of Total Probability states that if B1, B2, ..., Bn are mutually exclusive events that cover the entire sample space, then for any event A, P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn).

Front

What is the difference between independent and dependent events?

Back

Independent events are events where the occurrence of one does not affect the probability of the other. Dependent events are events where the occurrence of one event affects the probability of the other.

Tags

CCSS.HSS.CP.A.5

Front

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

Back

If A and B are independent, then 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 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 at least one event occurring?

Back

To find the probability of at least one of several events occurring, use the formula: P(at least one) = 1 - P(none).

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 a sample space?

Back

A sample space is the set of all possible outcomes of a random experiment.