Useful Fact Sheet Exam 2- Chapter 3 and 4
Classical (or Theoretical) Probability
Empirical (or Statistical) Probability
The Sum Rule
• The sum of the probabilities of all the simple events in the sample space must equal 1.
The Complement Rule
• The complement of event E is the event that E does not occur, denoted by Ecor E’
The compliment of E is the set of all outcomes in S that are not in E.
P(E’) = 1 – P(E)
P(E) +P(E’) = 1
Probability of Occurrence of both Events A and B
Probability of Occurrence of either Events A or B
Conditional Probability
Independent Events
.
Two event s A and B are called dependent events if the occurrence of event B has changed the
probability that event A will occur, that is
Intersection of Sets – The intersection of sets A and B, written A⋂B, is the set of elements common in
both A and B, or
Union of Sets – The union of sets A and B, written A⋃B, is the set of elements belonging to wither of the
sets, or
Disjoint Sets (Mutually Exclusive) – Two sets have no elements in common, sets A and B are disjoint if
A⋂B = ø.
Permutations of n objects taken r at a time:
Distinguishable Permutations: n1 alike, n2 alike … nk alike:
Permutations of n objects taken r at a time:
The Factorial
Mean of a Discrete Random Variable:
also called the Expected Value
Variance of a Discrete Random Variable:
Standard Deviation of a Discrete Random Variable:
Binomial Probability of x successes in n trials
P( x)  n C x p x q n  x 
Population Parameter of a Binomial Distribution:
Mean:
Standard Deviation:
Variance:
n!
p x q n x .
x !(n  x)!