AP Stats Chapter 14.notebook
December 11, 2014
Chapter 14: Probability
Random Phenomenon: a phenomenon is random if you know what outcomes could happen, but not which will happen.
Trial: Each occasion where we observe a random phenomenon
Outcome: The value of each trial
Event: combining outcomes (passing as opposed to an individual letter grade). Each individual outcome is also an event.
Sample Space: Collection of all possible outcomes.
For a test grade S = {A,B,C,D,F}
Law Of Large Numbers: If events are independent it says that as the number of trials increase the relative frequency of repeated events gets closer and closer to a single number. That value is called the probability of the event. A probability based on relative frequency (repeated trials) is known as empirical probability.
WARNING! WARNING! DANGER WILL ROBINSON...
THERE IS NO LAW OF AVERGAGES!!!!
Each individual trial of independent events has the same probability of occuring....it has nothing to do with previous results!
AP Stats Chapter 14.notebook
December 11, 2014
Modeling Probability:
When we actually use math, as opposed to observations, to determine the probability of an event it is called Theoretical Probability.
Notation information: The probability of an event is represented by a capital "P" and then some simple description of the event.
P(A) or P(1) or P(x > 12)
The basic form of the Theoretical Probability formula is...
P(A) = number of desired outcomes (ways A can happen)
total number of possible outcomes
For a standard deck of cards (no jokers)
P(jack) =
P(red) =
P(spades) =
P(card < 10) =
P(red ace) =
P(Jack of Diamonds) =
P(Face card) =
AP Stats Chapter 14.notebook
December 11, 2014
We use probability terminology and estimation all the time:
"I'm 30% sure I will go to the game."
"There's a 1 in ten chance that I passed that test."
"I'd say there is a one in a million chance she would go out with you." "So, you're saying there's a chance."
This type of probability is, obviously, very subjective and known as Personal Probability.
Venn Diagrams are a great tool for probability (especially when looking at if events are mutually exclusive.)
blue"
AP Stats Chapter 14.notebook
December 11, 2014
AP Stats Chapter 14.notebook
December 11, 2014
AP Stats Chapter 14.notebook
December 11, 2014
AP Stats Chapter 14.notebook
December 11, 2014
Some rules of Probability:
1.) A probability is a number between 0 and 1
0 < P(A) < 1 2.) The sum of the probabilities of all possible outcomes for an event is 1
P(S) = 1
(Probability Assignment Rule)
3.) The set of outcomes that are not in the desired event is called the complement of A and is denoted as Ac. The sum of an event (A) and its complement (Ac) is 1
P(A) = 1 ­ P(Ac)
(Complement Rule)
4.) If two events are disjoint or mutually exclusive then the
probability of one or the other happening is the sum of their probabilities. Disjoint or mutually exclusive events have no common outcomes (can't both happen at the same time)
P( A U B) = P(A) + P(B), provided A and B are disjoint
Addition Rule
A
B
When dealing with a sample
space that is made up of disjoint events the sum of
all probabilites must be 1
If events are disjoint they are not INDEPENDENT
AP Stats Chapter 14.notebook
December 11, 2014
5.) The probability of two independent events both occurring is the product of thei probailities
U
P(A B) = P(A) X P(B) provided A and B are independent
Multiplication Rule
Not Rule 4 is for mutually exclusive events and Rule 5 is for independent events...what do we do if they are not mutually exclusive or independent?
Well, I'll tell you what.............
We wait for next chapter!!!
Assignment: Page 338­341
#1,2,7,13,19,21,25,26,32,37,38,44
AP Stats Chapter 14.notebook
December 11, 2014