Probability II

Question 1

Process of obtaining an outcome.

Answer 1

Trail

Question 2

The individual possibility that occurs on each trial.

Answer 2

Outcome.

Question 3

Specific collection of outcomes.

Answer 3

Event.

Question 4

Collection of all possible outcomes.

Answer 4

Sample Space.

Question 5

What is a Probability?

Answer 5

Numerical measure of likelihood that an outcome or event will occur. P(A). Lies Between 0 & 1. Sum of Probabilities is 1.

Question 6

What are the 3 methods of assigning event probabilities?

Answer 6

1. a priori (Classical Method). 2. Relative Frequency Method. 3. Personal Probability Method.

Question 7

A priori meaning.

Answer 7

Knowledge is obtained by analyzing concepts independent of experience. Ex. All bachelors are unmarried, mathematics. These can be derive by reason alone.

Question 8

A posteriori meaning.

Answer 8

Knowledge is obtained through experience. Athletics.

Question 9

Which method uses prior knowledge of the process, done before the experiment, and P(Event) = X / T; S is the number of event outcomes and T is the number of outcomes equally likely.

Answer 9

A priori, classical method.

Question 10

Which method collects actual data, the probability is determined after the trail, and P(Event) = X / T; X is repeated number of times of the trail and X is the number of times the event is observed.

Answer 10

Relative Frequency Method.

Question 11

This assures the relative frequency method.

Answer 11

The Law of Large Numbers.

Question 12

Two or more events happening at the same time.

Answer 12

Compound events.

Question 13

Numerical measure of likelihood that compound event (two or more events) will occur.

Answer 13

Compound event probability.

Question 14

These three formula methods are used to determine compound event probability but simplify when considering disjoint and independent events.

Answer 14

Addition Rule, Conditional Probability Formula, and Multiplication Rule.

Question 15

When is the addition rule used and what is the formula?

Answer 15

It is used to get compound probabilities for union of events and/or not knowing if A & B are disjoint.

P(A or B) = P(A) + P(B) - P(A U B).

For Disjoint Events, then P(A or B) = P(A) + P(B).

Question 16

What type of probability is P(A|B) and what is the formula to solve?

Answer 16

P(A|B) is a conditional probability and is read as, the probability of A given B.

The liklihood of A occuring given that B occurs.

P(A|B) = P(A and B) / P(B).

P(B|A) = P(B and A) / P(A).

Question 17

Statistical Independence.

Answer 17

Event occurrence does NOT affect probabiliry of another event.

Causality not implied.

Question 18

What are the test for independence?

Answer 18

P(A|B) = P(A)

P(B|A) = P(B)

P(A and B) = P(A)*P(B).

Question 19

When is the mulitplication rule used and what is the formula?

Answer 19

It is used to get compund probabilities for Intersection of events.

P(A and B) = P(A)* P(B|A) = P(B)*P(A|B).

For independent events, P(A and B) = P(A)*P(B).

Question 20

Complement Rule.

Answer 20

Complement of Event

For Event A, All Events Not In A: A^c

P(A) = #, P(A^c) = 1 - P(A).