Chapter 3: Probability Theory

Question 1

Probability Theory is a branch of

Answer 1

A branch of Mathematics concerned with the analysis of random phenomena.
It gives you the tools to describe things around you that are random.

Question 2

Experiment

Answer 2

any repeatable process from which an outcome, result or measurement is obtained.

Question 3

Random Experiment

Answer 3

an experiment that produces a definite outcome that cannot be predicted with certainty

Question 4

Trial

Answer 4

one repetition of a Random Experiment

Question 5

Sample Space

Answer 5

set of all possible outcomes based on a random experiment

Question 6

1. Event

2. An Event (E) is said to occur…

Answer 6

subset of a sample space: any set of outcomes. 
An event (E) is said to occur on a particular trial of the experiment if the outcome observed is an element of the set (E).

Question 7

Simple Element

Answer 7

any basic outcome from a random experiment

Question 8

composite element

Answer 8

any combo of 2 or more basic outcomes from a random experiment.

Question 9

Probability of an outcome (e) in the sample space (s)

Answer 9

a number p between 0 and 1 that measures the likelihood that (e) will occur in a single trial of a random experiment.

Question 10

Probability of an event (A) denoted by P(A)

Answer 10

is the sum of all the probabilities of the individual outcomes of which it is composed.

Question 11

Permutation

Answer 11

a permutation of n different things taken x at a time is an arrangement in a specific order of any x of n things

Question 12

combination

Answer 12

a combination of n things taken x at a time is an arrangement of any x of these things in no particular order.

Question 13

A ∩ B (and)

Answer 13

collection of all outcomes that are elements of the sets A and B

Question 14

Mutually Exclusive: P(A∩B)=0

Answer 14

Events A and B are mutually exclusive or disjoint if they have no elements in common.
Impossible for A and B to occur simultaneously.

Question 15

A U B (or)

Answer 15

collection of all outcomes of both A and B, or one of them.

Question 16

Additive Rule

Answer 16

P(AUB) = P(A)+P(B)-P(A∩B)

Question 17

Special Addition Law

Answer 17

For any 2 mutually exclusive events:

P(AUB)=P(A)+P(B)

Question 18

Complements

Answer 18

The complement of an event are all elements in the sample set that are not a part of the event.
P(A’) = 1 - P(A)

Question 19

Unconditional Probability

Answer 19

The likelihood that a particular event will occur, regardless of whether or not another event occurs

Question 20

Conditional Probability

Answer 20

The Probability that an event has occurred in a trial of a random experiment given that another event B has also occurred

p(A|B) = p(A ∩ B) / p(B) .

Question 21

Joint Probability

Answer 21

the likelihood that 2 events occur at the same time

Question 22

Collectively exhaustive events

Answer 22

Set of events is collectively exhaustive is the union contains all the basic outcomes of the sample space
A and A’ are collectively exhaustive and mutually exclusive

Question 23

Partition

Answer 23

events that are collectively exhaustive and mutually exclusive

Question 24

Joint probability table

Answer 24

Shows frequencies or relative frequencies for joint events

Question 25

When would you use Baye's Theorem?

Answer 25

If you have a hypothesis, You've looked at evidence, You want to find the probability that your hypothesis is true, given that the evidence is also true.