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

Back

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the relationship between independent events and conditional probability?

Back

If A and B are independent events, then P(A|B) = P(A). This means the occurrence of B does not affect the probability of A.

Tags

CCSS.HSS.CP.A.3

Front

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

Back

It means that if event B occurs, there is a 30% chance that event A will also occur.

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

How can conditional probability be used in real-life scenarios?

Back

It can be used in various fields such as medicine (to determine the probability of a disease given a positive test result), finance, and risk assessment.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the difference between P(A|B) and P(B|A)?

Back

P(A|B) is the probability of A given B, while P(B|A) is the probability of B given A. They are not generally equal.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5