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 reads as '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

The formula for Conditional Probability is: P(A|B) = \frac{P(A \cap B)}{P(B)} where P(A \cap 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 it mean for two events to be independent?

Back

Two events A and B are independent if the occurrence of one does not affect the probability of the other. Mathematically, this is expressed as P(A|B) = P(A) and P(B|A) = P(B).

Tags

CCSS.HSS.CP.A.3

Front

How do you determine if two events are independent?

Back

To determine if two events A and B are independent, check if P(A \cap B) = P(A) * P(B). If this equality holds, the events are independent.

Tags

CCSS.HSS.CP.A.4

CCSS.HSS.CP.A.2

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

What is the probability of the complement of an event?

Back

The probability of the complement of an event A is calculated as: P(A') = 1 - P(A). This means if you know the probability of an event, you can find the probability of it not happening.

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 Bayes' Theorem?

Back

Bayes' Theorem relates the conditional and marginal probabilities of random events. It is expressed as: P(A|B) = \frac{P(B|A)P(A)}{P(B)}.

Front

How do you calculate the probability of an event given another event?

Back

To calculate the probability of event A given event B, use the formula: P(A|B) = \frac{P(A \cap B)}{P(B)}.

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

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5