Fundamentals of Probability

Question 1

What is a sample space

Answer 1

It is a collection of all possible outcomes of an experiment, denoted as “S”

Question 2

What is an event

Answer 2

it is any collection of outcomes of the experiment denoted as “A”, “B”, etc.
Includes individual outcomes, the null set, the entire sample space

Question 3

What do we call an outcome that is a member of an event

Answer 3

The is event is said to have occurred

Question 4

What is probability

Answer 4

A scientific way to measure uncertainty

Question 5

What is a set?

Answer 5

is a collection of objects. Denoted with capital letter. for example A={a,b,c,…,z}

Question 6

What is an element

Answer 6

An element is a part of a set. for example z epsilon A says z is an element of a set A

Question 7

What is a countable set

Answer 7

is a set where you can count the number of elements in a set. In other words if you can assign a natural number to the elements of the set then it is countable

Question 8

What is an empty set/null set

Answer 8

A set that doesn’t have elements { } or 0crossed out. An empty set is always a subset of every set.

Question 9

What are the types of countable sets

Answer 9

Finitely Countable or Infinitely countable.

Question 10

Finitely countable set

Answer 10

D= {0,1,2,…10]

Question 11

Infinitely countable set

Answer 11

The set of natural numbers N = {1,2,3,…}

Question 12

What’s the subset concept

Answer 12

A is a subset of B if every element in A is also in B. for example A={x,y,z} B={w,x,y,z} A (c underlined) subsest B

Question 13

How do you calculate the number of subsets in a set

Answer 13

2^n where n is the number of elements

Question 14

Equal sets

Answer 14

A and B are equal if A c underline (subset) B and B c underline (subset) of A

Question 15

Intersection of event

Answer 15

it is the “and” of two events. for example AB is a set that contains elements in both A and B. for example
A={2,4,6} B = {4,5,6,7,8}
AB = {4,6}

Question 16

Union of events

Answer 16

it is the “or”.

AUB is a set that contains elements in either A or B. For example AuB={2,4,6,7,8} when we have A={2,4,6} B = {4,5,6,7,8}

Question 17

A complement or exhaustive

Answer 17

is an element outside of the set. We usually use exhaustive

Question 18

If AcB then…

Answer 18

AUB=B
A={1,2,3} B={1,2,3,4,5,6}
AUB={1,2,3,4,5,6}

Question 19

If AcB and BcA then…

Answer 19

then A=B

A={1,2,3} B={1,2,3}

Question 20

If AcB then…

Answer 20

then AB=A

A={1,2,3} B={1,2,3,4,5,6} then AB={1,2,3}

Question 21

if AUAc then

Answer 21

= S (the sample space). A union of A complement

Question 22

A and B are mutually exclusive it..

Answer 22

they don’t have any outcomes in common. aka disjoint

Question 23

Their union is equal to the sample space, but they have no events in common.

Answer 23

Groups of events that are mutually exclusive and exhaustive

Question 24

A and B are mutually exclusive and exhaustive

Answer 24

AUB = S but they have no events in common. It means that they make up the entire sample space but have no common events

Question 25

A probability on a sample S is

Answer 25

We assign every event A a number P(A), which is the probability the event will occur (P:S—>R).
A collection of numbers P(A) that satisfy these axioms:
1. P(A) >=0 for all AcS
2. P(S) =1
3. For any sequence of disjoint sets (A1, A2, A3,…, this could be an infinite sequence) The probability of the union of that sequence is equal to the probabilities of those events. P(UiAi)=SigmaiP(Ai)

Question 26

P(Ac) =

the probability of A compliment

Answer 26

1-P(A)

Question 27

P( ) =

probability of empty set

Answer 27

0

Question 28

If AcB then

Answer 28

P(A)<=P(B)

Question 29

For all A

Answer 29

0<=P(A)<=1

Question 30

P(AUB)=

Answer 30

P(A) + P(B) - P(AB)

Question 31

P(ABc) =

probability of AB compliment

Answer 31

P(A)-P(AB)

Question 32

What is the definition of Combinatronics

Answer 32

Counting Rules - fancy counting

Question 33

What are the combinatronics

Answer 33

1. If an experiment has two parts, first one having m possibilities and regardless of the outcome in the first part, the second one having n possibilites, then the experiment has m*n possible outcomes
2. An ordered arrangement of objects is called a permutation. The number of different permutations of N objects is N!. The number of different permutations of n objects taken from N objects is N!/(N-n)!
3. Any unordered arrangement of objects is called a combination. The number of different combinations of n objects taken from N objects is N!/{N-n)!n!}. this is typically denoted as (Nn)—>”N choose n”

Question 34

Permutation

Answer 34

any ordered arrangement of objects. The number of different permutations of N objects is N!. The number of different permutations of n objects taken from N objects is N!/(N-n)!

Question 35

Combination

Answer 35

Any unordered arrangement of objects. The number of different combinations of n objects taken from N objects is N!/{N-n)!n!}. we call this N choose n and it is denoted as
(N
n)

Question 36

A \ B is

Answer 36

This reads A set minus B and means a set containing all elements of A which are not elements of B.

Question 37

Independence

Answer 37

Events A and B are independent if the probability of their intersection is equal to the product of their probability in an equation it read P(AB) = P(A)*P(B)

Question 38

If A and B are independent, then A and B complete are

Answer 38

also independent

Question 39

Probability of A conditional on B is P(A|B) and is

Answer 39

P(AB)/P(B) assuming P(B)>0

T

Question 40

Baye’s Theorem

Answer 40

P(A|B) = P(B|A)P(A)/{P(B|A)(P(A) + P(B|A complement)P(A complement). As long as A and A complement form a partition of S

Question 41

Prior probability is also known as

Answer 41

the unconditional probability