Topic
Name: Delonta Holmes
Teacher: William Hawk
Class: Critical Thinking
Date 10/26/09
Questions/Main Ideas:
Notes
Probability Calculations
Cogent Inductive Arguments
Provide Probability
Deductive probability
Scale:
0 = event will not happen
1 = event will happen
between 0 & 1 = probability
Theories of Probability
Relative Frequency Theory – based on empirically determinate statistics
Subjective Theory – based on personal beliefs and experience
General Conjunction Rule
Used to calculate the probability of two or more dependent events.
Dependent events
= the occurrence of one has an effect on the probability of
the other.
P(A) x P(A given B) x P(N given A through N1)
Example: Drawing two aces from a deck
P = 4/52 x 3/51 = 12/1652 = .0045248%
Restricted Disjunctive Rule
Used to calculate two or more
mutually exclusive events.
P(A or B or N) = P(A) + P(B) +…P(N)
Example: Rolling a 4 or 6 on a die
P(4 or 6) = 1/6 + 1/6 = 1/3 = .3333%
General Disjunction Rule
Used to calculate that either of two or more events will occur.
P(A or B or…N) =
[P(A) + P(B) + …P(N)] – [P(A X B X …N)]
P(A or U) = (.63 + .52) – (.63 x .52) = (1.15  .3276) = .8224
Negation Rule
Tells the probability an event will occur given the probability that it will not
occur.
P(A) = 1 
P(NotA)
Example:
That aunt [.63] will die before 80
P(D) = 1  .63 = .37
Conditional Probability
Calculating the probability of B given A
P(A)
Example: Probability of drawing King if a face card has been drawn
P(K/F) =
4
= .3334
12
Generalizations and
Particularizations
Invalid Argument
Assessed in terms of strength
Possible that the premises are true and the conclusion is false.
Generalization
Argument concerning a population based upon observation of a
“representative” sample.
Strength of inductive argument
Depends upon
modesty
of conclusion.
Depends upon the
size
of the sample.
Depends upon the
diversity
of the sample.
Depends upon the degree to which the sample is
representative
of the
population
Particularization
Drawing inferences about a subset of a group based upon facts concerning the
entire population
of that group.
Form of Particularization
Arguments
Where
n
is a number between 0 and 100, and
x
is kind of thing, and
P
is some
property or relationship:
1.
n
percent of
x
’s have
P
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document2.
A
is an
x
3. Thus, there is an
n
* percent probability that
A
has
P
(where
n
* is
less than or equal to
n
)
Analogical Arguments
Form of Analogical Arguments
1. Objects
x
,
y
,
z
…all have properties
P
,
Q
,
R
,
S
…
2. Object
w
also has properties
Q
,
R
,
S
…
3. Thus, (probably) object
w
also has
P
.
Evaluating Analogical
Arguments:
Stronger Analogical Arguments
Have More .
..
1.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '10
 h
 Logic, Probability, analogical arguments

Click to edit the document details