Probablity Theory

Question 1

What is an experiement

Answer 1

A process for which a single outcome occurs but in which there is more than one possible outcome, thus we are uncertain which outcome will reult

Question 2

Structure of a playing card deck

Answer 2

52 cards
4 types : clubs spades, diamonds, hearts
26 black cards, 26 red cards
13 types of cards with 4 each: 2,3,4,5,6,7,8,8,10,J,Q,K,A

Question 3

What is the sample space

Answer 3

S
The set of all possible outcome of an experiement

Question 4

What is a probability model

Answer 4

A statistical model in which each outcome in a sample space is assigned a probability that describes the likley hood of that outcome where

1) o <= p(i) <= 1 for i = 1,2,…,n
2) sum where i starts at 1 and ends at n if p (i) =1

Question 5

What does the notation P (O) mean?

Answer 5

The portability of outcome O occurring

Question 6

Continuous vs Discrete Numbers

Answer 6

Continuous numbers are measurable, infinite, not countable (every number between x and y)
Discrete numbers are countable (1,2,3,4)

Question 7

What is replacement

Answer 7

Recreating the initial conditions after an event
Ex: drawing a cards and then replacing the card

Without replacement means keeping the changed conditions in future trials which can effect the total number of objects in the pool

Question 8

What is a probability value

Answer 8

The likley hood of an event occurring

Question 9

What is the probability in a fair game or a fair draw or anything fair

Answer 9

1/n where n is the number of items in the pool

Question 10

What is an event

Answer 10

A subset of a sample space which contains an outcome or many outcomes of interest

Question 11

What is the probability of an event

Answer 11

The sum of the probabilities of each individual outcome in the event occurring

Question 12

Can the probability of an event ever be greater than 1

Answer 12

No since the sum of all outcomes in a sample space adds to one, so there can be no combination of additions which result in a greater probability then 1
If P(A) = 1 then P(A) = P(S)

Question 13

What is a compliment

Answer 13

Everything not contained within a given event
NOT
The probabilities of an event and it’s compliment = 1

Question 14

What is the intersection of two events

Answer 14

AND
A n B - Includes all outcomes common to both events
P (A n B) is the probability that both events occur simultaneously

Question 15

(T/F) A n B != B n A

Answer 15

F

Question 16

.. A n A’ = null set

Answer 16

T

Question 17

.. P(A n A’) = 0

Answer 17

T

Question 18

.. P (A n B ) + P (A n B ‘ ) = P (B)

Answer 18

F
P (A)

Question 19

.. A n (B n C) = (A n B ) n C

Answer 19

T

Question 20

What are mutually exclusive events

Answer 20

Either
Two events that have no outcome in common
A n B = {} empty set
P ( A n B) = 0
Both events can not occur simultaneously

Question 21

What is the union of events

Answer 21

OR
The probability that at least one of A or B occurs - A occurs, B occurs, they both occur are included

Question 22

What is (A U B)’

Answer 22

A’ n B’

Question 23

IF a C b, A U B =

Answer 23

B

Question 24

A U B

Answer 24

B U A

Question 25

A U null set

Answer 25

A

Question 26

A u A’

Answer 26

S

Question 27

A u S

Answer 27

S

Question 28

(A U B) u C =

Answer 28

A u (B u C)

Question 29

What is P(A U B) if A and B are mutually exclusive

Answer 29

P (A) + P (B)

Question 30

What is a partition

Answer 30

A sequence of A1, A2, … An mutually exclusive events where A1 u A2 … An = S
Each outcome in S is contained in one event and these events can be added to create S

Question 31

What is conditional probability

Answer 31

The probability of an event occurring conditional on event B has occurred

P (A|B) = P (A n B)/ P (B) where P(B) > 0

Question 32

(A U B ) ‘ =

Answer 32

A’ n B’