chapter 1

Question 1

the process which an observation (or measurement) data is obtained through either uncontrolled events in nature or controlled situations in a laboratory.

Answer 1

Experiment

Question 2

the set whose elements are all the possible outcomes of an experiment.

Answer 2

Sample Space

Question 3

elements in a sample space.

Answer 3

Sample Points

Question 4

has a finite number of outcomes.

ex. Outcomes of a single coin tossed

Answer 4

Finite Sample Space

Question 5

has an infinite number of outcomes.

ex. Waiting time at the bus stop

Answer 5

Infinite Sample Space

Question 6

a subset of the sample space.

Answer 6

Event

Question 7

an event that contains one
sample point.

Answer 7

Simple Event

Question 8

has no outcomes,
cannot occur.

Answer 8

Null Space {} or Empty Set Ø

Question 9

What are the three (3) set operations?

Answer 9

Union, intersection, complement

Question 10

Set Operations

The ________ of two events consists of all outcomes that are contained in one event or the other, denoted as 𝑬𝟏∪𝑬𝟐.

Answer 10

Union

Question 11

Set Operations

The ________ of two events consists of all outcomes that are contained in one event and 𝑬𝟏∩𝑬𝟐.

Answer 11

Intersection

Question 12

Set Operations

The _____________ of an event is the set of outcomes in the sample space that are not contained in the event, denoted as 𝑬’

Answer 12

Complement

Question 13

Events A and B are ______________________ or disjoint because they share no common outcomes.

Answer 13

mutually exclusive

Question 14

The occurrence of one event precludes the occurrence of the other.

Answer 14

mutually exclusive

Question 15

Symbolically, A ∩B = Ø

Answer 15

mutually exclusive

Question 16

mutually exclusive

A∪B= B∪A and A∩B= B∩A

Answer 16

Commutative Law (Event Order Is Unimportant)

Question 17

mutually exclusive

(A ∪B) ∩ C= (A ∩ C) ∪(B∩C)
(A ∩B) ∪ C= (A∪ C) ∩(B∪C)

Answer 17

Distributive Law

Question 18

mutually exclusive

(A ∪B) ∪ C = A ∪(B ∪ C)
(A ∩B) ∩ C= A ∩(B∩C)

Answer 18

Associative Law (Like In Algebra)

Question 19

mutually exclusive

(A ∪B)’ = A’∩ B’ the complement of the union is the intersection of the complements.

(A ∩B)’= A’∪B’ the complement of the intersection is the union of the complements

Answer 19

Demorgan’s Law

Question 20

mutually exclusive

(A’)’ = A

Answer 20

Complement Law

Question 21

The negation of a disjunction is the conjunction of the negations;

The negation of a conjunction is the disjunction of the negations;

True or false?

Answer 21

throat.

Question 22

Basic Counting Techniques

There are three special rules, or counting techniques, used to determine the number of outcomes in events. They are :

Answer 22

1. Multiplication rule
2. Permutation rule
3. Combination rule

Question 23

Basic Counting Techniques

“If a certain experiment can be performed in n1 ways and corresponding to each of these ways another experiment can be performed in n2 ways, then the combined experiment can be performed in n1* n2ways.”

Answer 23

Multiplication rule

Question 24

Basic Counting Techniques

Arrangement of objects w/ regards to order.

Answer 24

Permutation

Question 25

Give 4 kinds of permutation

Answer 25

1. Linear Permutation (Factorial Method)
2. Permutation nPr, Permutation of Subsets.
3. Permutation of Similar Objects, Permutation with repetition.
4. Circular Permutation

Question 26

PERMUTATION OF DISTINCT OBJECTS

The number of permutations of n distinct objects is n!

Answer 26

Factorial method

Question 27

PERMUTATION OF DISTINCT OBJECTS

The number of permutations of n objects taken r at a time is

Answer 27

Permutation (nPr)/ Permutation of Subsets

Question 28

PERMUTATION OF DISTINCT OBJECTS

The number of permutations of n distinct objects arranged in a circle is ________________.

Answer 28

Circular Permutation

Question 29

PERMUTATION OF DISTINCT OBJECTS

The number of distinct permutations of n distinct objects of which n1 are of the first kind, n2 of the second kind, …, nk of the kth kind.

Also applicable for partitioning or groupings of all the n objects.

Answer 29

Permutation with Repetition

Question 30

The _____________ of n objects taken at r at a time, where order does not count, is C(n,r) or nCr.

Answer 30

combination

Question 31

2 special cases for permutation.

Answer 31

1. Clustering/grouping.
2. Complement of 1.

Question 32

Additive rule for permutation/combination

(using phrases “greater/more than” & “less than”)

Answer 32

Exclusive Range

Question 33

Additive rule for permutation/combination

(using phrases “at most” & “atleast”)

Answer 33

Inclusive Range

Question 34

_______________ is the likelihood or chance that a particular outcome or event from a random experiment will occur.

Answer 34

Probability

Question 35

Probability is a number in the ____ interval

Answer 35

[0,1]

Question 36

A probability of:

1 means __________
0 means _______________

Answer 36

certainty, impossibility

Question 37

It is a number that is assigned to each member of a collection of events from a random experiment that satisfies the axioms of probability.

Answer 37

Probability

Question 38

____________ are generated by applying basic set operations to individual events,

Answer 38

Joint events

Question 39

Probabilities of joint events can often be determined from the probabilities of the individual events that comprise them.

true or false?

Answer 39

True

Question 40

The ____________________ of an event A given the occurrence of an event B is defined as P(A| B)

Answer 40

Conditional Probability

Question 41

P(A∩B) = P(B|A)·P(A) = P(A|B)·P(B)

Answer 41

Multiplication Rule

Question 42

P(F) = P(F | H)∗P(H) + P(F | M) ∗ P(M) + P(F | L) ∗ P(L)

Answer 42

Total Probability Rule

Question 43

Two events are _______________ if any one of the following equivalent statements is true:

1. P(A|B)=P(A)
2. P(B|A)=P(B)
3. P(A∩B)=P(A)·P(B)

This means that occurrence of one event has no impact on the probability of occurrence of the other event.

Answer 43

independent

Question 44

________________ (1702-1761) was an English mathematician and Presbyterian minister.

His idea was that we observe conditional probabilities through prior information.

Answer 44

Thomas Bayes