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Probability

Terms in this set (34)

Probability
# ofways an event can happen/Total#ofoutcomes
P(A)=n(A)/n(S)
Sample Space
All possible outcomes of an experiment
Picking a card from deck = Sample Space of 52
Uniform Probability
All outcomes are equally likely. A deck of cards has a uniform distribution because the likelihood of drawing a heart, club, diamond or spade is equally likely. A coin also has a uniform distribution because the probability of getting either heads or tails in a coin toss is the same.
NON Uniform Probability
Rolling a weighted dice
Picking from a bag of marbles with uneven #s of colors
Fundamental Counting Principle
When there are m ways to do one thing,
and n ways to do another,
then there are m×n ways of doing both
Intuitive Probability/Subjective Probability
The probability of event A =
# times event A can occur/total #of occurrences
Universal Set
All elements defined by that set
Outcome
A subset of a universal set
Subset
A collection of elements that all exist within another set
Empty or Null Set
No elements fit that description
Complement of an event
The possibility of everything but that event occurring
Mutually Exclusive or Disjoint Sets
The events cannot occur at the same time. For example you can't flip a head and a tail at the same time
Intersection
Collection of elements that are COMMON between the sets (symbol looks like rainbow)
Union
Collection of all elements from both sets. (Symbol looks like a U)
Compound Probability
Performing more than one event in a sequence (2 or more probabilities)
Rolling a 6 and getting a head coin flip
Independent Event
If A occurs and it doesn't affect B occuring
Rolling a dice and Flipping a coin
NOT Dependent
The second selection is affected by the first
7 Chocolate Chip and 3 Peanut Butter Cookies
if you pick a chocolate chip out first the probability of getting a peanut butter cookie goes from 1/10(total # of cookies to start) to 1/0
Multiplication Rule
Find the probability of each event separately, then multiply the probabilities
Mutually exclusive set
Share no elements
Independent set
Sets do not impact each others probabilities
Replacement
Events are Independent
No Replacement
NOT Independent
Test for Independence
P (A and B) = P(A) *P(B)
Conditional Probability
P(B|A) means "Event B given Event A"
Example: Drawing 2 Kings from a Deck

Event A is drawing a King first, and Event B is drawing a King second.

For the first card the chance of drawing a King is 4 out of 52

P(A) = 4/52

But after removing a King from the deck the probability of the 2nd card drawn is less likely to be a King (only 3 of the 51 cards left are Kings):

P(B|A) = 3/51

And so:

P(A and B) = P(A) x P(B|A) = (4/52) x (3/51) = 12/2652 = 1/221

So the chance of getting 2 Kings is 1 in 221, or about 0.5%
Conditional Probability Independent Event
P(A|B) = P(A), or, which is the same
P(B|A) = P(B). To find the probability of two independent events that occur in sequence, find the probability of each event occurring separately, and then multiply the probabilities. This multiplication rule is defined symbolically below. Note that multiplication is represented by AND.

Multiplication Rule 1: When two events, A and B, are independent, the probability of both occurring is:
P(A and B) = P(A) · P(B)
Testing for Independence
If this statement is true when you solve the probability then they are independent
P(A|B) = P(A), or, which is the same
P(B|A) = P(B).
Two Way Frequency Table
Used when there are two different categories of data
Marginal Frequencies
Those numbers in the total column
Joint Frequences
Entries in the body of the table
Compound Probability Intersection
The intersection is found at the intersection of the row and colum
Two way relative frequencey table
Two way relative frequency tables will ALWAYS HAVE 1
as the sum of the row and column marginal values.
Conditional probability
The calculation of a probability that follows a previous event
Conditional probability dependence
What is the probability of getting a number greater than 4 on a die, GIVEN THAT the roll was even?
Conditional probability mutually exclusive
No elements in common answer will be zero from the formula
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