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 A given 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

How do you calculate Conditional Probability?

Back

Conditional Probability can be 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.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What is the difference between independent and dependent events?

Back

Independent events are those whose outcomes do not affect each other, while dependent events are those where the outcome of one event affects the outcome of another.

Tags

CCSS.HSS.CP.A.5

Front

If P(A) = 0.5 and P(B) = 0.3, what is P(A and B) if A and B are independent?

Back

If A and B are independent, P(A and B) = P(A) * P(B) = 0.5 * 0.3 = 0.15.

Tags

CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4

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 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) = [P(B | A) * P(A)] / P(B).

Front

What is the probability of selecting a male given that a student likes sports?

Back

This is an example of conditional probability, denoted as P(male | sports). It requires data on the number of males who like sports.

Tags

CCSS.HSS.CP.A.3

CCSS.HSS.CP.A.5

Front

What does it mean if P(A | B) = P(A)?

Back

If P(A | B) = P(A), it indicates that events A and B are independent; the occurrence of B does not affect the probability of A.

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

Tags

CCSS.HSS.CP.A.1