Conditional Probability

Front

What is Conditional Probability?

Back

The probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which reads 'the probability of A given B'.

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 ∩ B) / P(B), where P(A ∩ B) is the probability of both A and B occurring.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What does P(A|B) represent?

Back

It 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

If P(A) = 0.5 and P(B) = 0.4, what is P(A|B) if P(A ∩ B) = 0.2?

Back

P(A|B) = P(A ∩ B) / P(B) = 0.2 / 0.4 = 0.5.

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, P(A|B) = P(A). The occurrence of B does not affect the probability of A.

Tags

CCSS.HSS.CP.A.3

Front

How do you interpret P(B|A)?

Back

It is 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 Law of Total Probability?

Back

It states that if B1, B2, ..., Bn are mutually exclusive events that cover the entire sample space, then P(A) = Σ P(A|Bi)P(Bi).

Front

What is Bayes' Theorem?

Back

Bayes' Theorem relates the conditional and marginal probabilities of random events. It is given by P(A|B) = [P(B|A) * P(A)] / P(B).

Front

What is an example of Conditional Probability in real life?

Back

Determining the probability of a person having a disease given a positive test result.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the significance of Venn Diagrams in Conditional Probability?

Back

Venn Diagrams visually represent the relationships between different events, helping to understand intersections and unions.

Tags

CCSS.HSS.CP.A.1