Probablity Theory Flashcards
What is an experiement
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
Structure of a playing card deck
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
What is the sample space
S
The set of all possible outcome of an experiement
What is a probability model
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
What does the notation P (O) mean?
The portability of outcome O occurring
Continuous vs Discrete Numbers
Continuous numbers are measurable, infinite, not countable (every number between x and y)
Discrete numbers are countable (1,2,3,4)
What is replacement
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
What is a probability value
The likley hood of an event occurring
What is the probability in a fair game or a fair draw or anything fair
1/n where n is the number of items in the pool
What is an event
A subset of a sample space which contains an outcome or many outcomes of interest
What is the probability of an event
The sum of the probabilities of each individual outcome in the event occurring
Can the probability of an event ever be greater than 1
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)
What is a compliment
Everything not contained within a given event
NOT
The probabilities of an event and it’s compliment = 1
What is the intersection of two events
AND
A n B - Includes all outcomes common to both events
P (A n B) is the probability that both events occur simultaneously
(T/F) A n B != B n A
F
.. A n A’ = null set
T
.. P(A n A’) = 0
T
.. P (A n B ) + P (A n B ‘ ) = P (B)
F
P (A)
.. A n (B n C) = (A n B ) n C
T
What are mutually exclusive events
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
What is the union of events
OR
The probability that at least one of A or B occurs - A occurs, B occurs, they both occur are included
What is (A U B)’
A’ n B’
IF a C b, A U B =
B
A U B
B U A
A U null set
A
A u A’
S
A u S
S
(A U B) u C =
A u (B u C)
What is P(A U B) if A and B are mutually exclusive
P (A) + P (B)
What is a partition
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
What is conditional probability
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
(A U B ) ‘ =
A’ n B’
