DISCLAIMER RANDOM SAMPLING AND 9/11/2013

9/11/2013
DISCLAIMER
RANDOM SAMPLING AND
PROBABILITY
Prepared by:
Jess Roel Q. Pesole
RANDOM SAMPLE
A sample selected from the population by a
process that ensures the following
characteristics:
(1) Each possible sample of a given size has an
equal chance of being selected
(2) All the members of the population have an
equal chance of being selected into the
sample
TYPES OF RANDOM SAMPLING
1.
2.
3.
4.
5.
Simple
Convenient
Systematic
Stratified
Cluster
• Due to time restrictions, this presentation will
condense the lessons discussed in Chapters 8
and 10 of the book by Pagano. Please make
sure to read the book to supplement your
knowledge of the subject matter.
WHY CONDUCT RANDOM SAMPLING?
(1) Applying the laws of probability, this process
is done in order to ensure that every person
has a probable chance of being part of the
sample
(2) It makes the sample representative of the
population.
PROBABILITY
• Relative likelihood of occurrence of any given
outcome or event
Probability
of an event
or outcome
=
Number of times the
outcome or event can
occur
Total number of times any
outcome or event can
occur
1
9/11/2013
PROBABILITY
RULES OF PROBABILITY
• Example: What is the probability
of drawing the Ace of Spades in a
shuffled pack of 52 cards?
Probability
of an event
or outcome
=
Number of
times the
outcome or
event can
occur
Total number
of times any
outcome or
event can
occur
=
1
52
≈ 0.0192 ≈ 0.02
PROBABILITY
• Example: What is the probability of
NOT drawing the Ace of Spades in a
shuffled pack of 52 cards?
Probability of an event or
outcome
=1-
Number of times the outcome or
event can occur
Total number of times any outcome
or event can occur
= 1 – (1/ 52)
≈ 1 – 0.0192
≈ 0.9808
≈ 0.98
RULES OF PROBABILITY
3. Multiplication rule - probability of obtaining a
combination of independent outcomes equals
the product of their separate probabilities
P(Ace in first draw and Queen in second draw)
= P(Ace in first draw) x P(Queen in second draw)
= 4/52 x 4/52
= 16/2704
≈ 0.0059
1. Converse rule - probability of an event not
occurring
- equals to 1 minus the probability of that
event occurring
Probability
of an event
or outcome
not
occurring
=
1-
Number of times the
outcome or event can
occur
Total number of times
any outcome or event
can occur
RULES OF PROBABILITY
2. Addition rule
Under the addition rule,
outcomes are considered as
mutually exclusive (no two
outcomes can occur
simultaneously).
Example: No single card from the
deck can be an ace of spade or a
queen of hearts at the same time.
RULES OF PROBABILITY
2. Multiplication rule
Under the multiplication rule, there
is the assumption of independent
outcomes (occurrence of one does
not change the likelihood of
another).
Example: Getting an ace of spades
in the first draw does NOT affect
getting the queen of hearts in the
second draw.
2
9/11/2013
EXERCISE
• Research has shown that 6 out of 10
marriages end in divorce. What is the
probability that
a. A particular just-married couple stays
married “until death do them part”?
b. Two couples married in a double ceremony
both get divorced?
EXERCISE
• A defendant in a criminal trial has a 0.42
probability of being convicted as charged, a
0.26 probability of being convicted of a lesser
charge, and a 0.32 chance of being found not
guilty.
a. What is the probability that a defendant
would be convicted of any charge?
ANSWERS
B.
A.
P (two couples divorce)
P (no divorce)
= P (divorce) * P
= 1 – P (divorce)
(divorce)
= 1 – (6 / 10)
= (6 / 10)*(6 / 10)
= 1 – 0.60
= 0.60 * 0.60
= 0.40
= 0.36
EXERCISE
A)
P (conviction in any charge)
= P (conviction as charged) + P
(conviction of a lesser charge)
= 0.42 + 0.26
= 0.68
EXERCISE
EXERCISE
• Suppose that 16% of inmates in Philippine
prisons have psychiatric illnesses. What is the
probability that
a. A particular prisoner does not suffer from a
psychiatric illness?
b. That three prisoners do not suffer from a
psychiatric illness?
• Suppose the mean IQ for a group of
psychopaths is 105 and the standard deviation
is 7. Assuming a normal distribution,
determine:
a. The percentage of IQ scores between 100
and 110
b. The probability of selecting a psychopath at
random who has an IQ between 100 and 110
3