Chapter 4 Notes

©2008 by S. Gramlich

Probability

! = Important Note

! These Notes are not meant to replace Reading. Read Chapter first.

4-2

Event = an outcome

Sample Space = all possible events

Probability = chance of an event happening (expressed either as a fraction, decimal, or %)

Probability of an Event A:

P(A) = s/n

s = # of ways A can or has occurred

n = sample size = total # of possible ways (count # events in sample space)

0 <= P(A) <= 1

complement of A = not A (Abar or A'): P(Abar)= 1 - P(A)

4-3

mutually exclusive (disjoint)= events cannot occur at same time (exclusive)

Addition Rule: P(A or B) = P(A) + P(B) - P(A ∩ B)

P(A ∩ B) = A and B at the same time

Contingency Table = Table with column and row variables

! add up the column and row totals first,

the sum of row totals = the sum of column totals = Grand Total = N = Sample Size

4-4

Differentiate between Independence and Dependence?

Independent = events aren't affected by each other, sampling done with replacement

Dependent = events are affected by each other, sampling done without replacement

Prob of A and THEN B:

P(A and B) = P(A)*P(B) if independent

P(A and B) = P(A)*P(B\A) if dependent

! use the s/n formula for calculating both events

P(B\A) = Prob of B occurring, given A has already occurred;

the sample size for calculating B will be 1 less than what was used for A if dependent