Conditional Probability

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 given event B.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the formula for Conditional Probability?

Back

The formula for Conditional Probability is P(A|B) = P(A ∩ B) / P(B), where P(A ∩ B) is the probability of both events A and B 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

How do you interpret P(B|A)?

Back

P(B|A) represents the probability of event B occurring given that event A has occurred.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the relationship between independent events and Conditional Probability?

Back

For independent events, the occurrence of one event does not affect the probability of the other. Thus, P(A|B) = P(A) and P(B|A) = P(B).

Tags

CCSS.HSS.CP.A.3

Front

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

Back

If A and B are independent, then P(A|B) = P(A) = 0.5.

Tags

CCSS.HSS.CP.A.3

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

Tags

CCSS.HSS.CP.A.1

Front

How do you calculate the probability of the union of two events?

Back

The probability of the union of two events A and B is given by P(A ∪ B) = P(A) + P(B) - P(A ∩ B).

Tags

CCSS.HSS.CP.B.7

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