Week 5 Material

True/False: If event A and event B are mutually exclusive, then P(A ∩ B) = P(A)*P(B)

FALSE

What is the equation for any two non-disjoint events A and B?

P(A U B) = P(A) + P(B) - P(A∩B)

True/False: If A and B are Conditionally Independent given C, then learning the outcome of B adds no new information regarding A if the outcome of C already is known.

TRUE

True/False: Independence in one direction implies independence in the other direction If P(Ai│Bj) = P(Ai), then P(Bj│Ai) = P(Bj)

TRUE

What is the equation for any three non-disjoint events A, B and C?

P(AUBUC) = P(A) + P(B) + P(C) - P(A∩B) - P(B∩C) - P(A∩B∩C)

When two events, A and B, are independent, what is the probability of both occurring?

P(A∩B) = P(A)*P(B)

What is the equation for the probability of B happening when A has also occurred; Stated as "The probability of B given A"?

P(B│A) = P(A and B) / P(A) ≠ P(B)

Conditional Probability

The probability of an event given that some other event has already occurred.

What is an Experiment (Random Experiment)

Any action or process whose outcome is subject to uncertainty. The process leads to the occurrence of one and only one of several possible outcomes.

What is Sample Space?

The set of all possible outcomes of an experiment..

True/False: Independent chance events are not the same as mutually exclusive outcomes.

TRUE

When P(A) and P(B) are mutually exclusive, are they independent?

"No, therefore if P(B) = P(A∩B) / P(A) or: if P(A) = P(A∩B) / P(B) or if P(B│A) = P(B) or

Let A and B be two events. If A and B are mutually exclusive, then which of the following expressions is true?

P(A U B) = P(A) +P(B)

Let A and B be two events. If A and B are independent than which of the following expressions is true?

P(A U B) ≤ P(A) + P(B)

When two events, A and B, are dependent, what is the probability of both occurring?

P(A∩B) = P(A) * P(B│A), where P(B│A) is the conditional probability

What are the axioms of probability?

1. For any event A, 0 ≤ P(A) ≤ 1 ; 2.Probabilities must add up: If A1, A2, A3,...is an infinite set of disjoint sets, then P(A1 U A2 U A3 U...)= ƩP (Ai) ; 3. Total Probability must equal one: P(S) = 1

What is a Venn Diagram

A graphic interpretation of set theory principles that can be used to illustrate the principles of probability.

What is Independence?

A property of probability where the occurrence of one event does not change the likelihood of another event occurring. In other words, if the occurrence of one event gives no information about another event, then the two events are independent. (ie. If P(A/B)=P(A), then A and B are independent).

What is an Event?

A set of outcomes that are a subset of the sample space.

Let A and B form a partition on our sample space S, then which of the following are true?

A union B = S, An intersection then B = null set, Both A and B are dependent

Complement of an Event

All the outcomes in the Sample Space that are not contained in the Event.

What is a Simple Event

An event that consists of exactly one outcome.

What is a Compound Event?

An event that consists of more than one outcome.

For Independence, the probability of outcome A occurring stays the same no matter which outcome of B has occurred.

P(Ai) = P(Ai│Bj) = P(Ai and Bj) / P(Bi) where P(Ai and Bj) = P(Ai)*P(Bj)

What is the equation for the probability of A happening when B has also occurred; Stated as "The probability of A given B"?

P(A│B) = P(A and B) / P(B) ≠ P(A)

True/False: two chance events being probabilistically dependent does not imply a casual relationship.

TRUE