Download Lecture covering Chapter 13-14 (3/1/05) -- Probability

STAT 1301
Introduction to Probability
Statistics:
The Science of Decision Making
in the Face of Uncertainty

Uncertainty makes life challenging
and interesting
– very few things are absolutely certain
Chance Situations
 Flip coin -- What is the chance of
heads?
 What is the chance that SMU’s
football team wins the rest of its
games?
 Weather tomorrow -- Rain?
Mathematical treatment of chance has roots
in gambling. Games of chance are ideal
examples.
3 Ways to Calculate Chance
(1) Classical (Theoretical)

Chance situation - N = total number of possible
occurrences (equally likely)
X = number of occurrences which
result in outcome
X
Chance[outcome] =
x 100%
N
Drop Thumbtack
Chance it lands “point down” = ?
3 Ways to Calculate Chance
(2) Frequency (Long Run)

Chance of an outcome is the percent of
times the outcome occurs when the
procedure is repeated over and over,
independently and under the same
conditions.
3 Ways to Calculate Chance
(3) Subjective (Degree of Belief)
Facts About Chance
Probability is chance expressed as a fraction
Virtual Impossibility
Chance = 0%
Probability = 0
Virtual Certainty
Chance = 100%
Probability = 1
Chance[ outcome does not occur ]
= 100%- Chance[ outcome does occur ]
IN GENERAL:
Chance[ something ]
=100% - Chance[ opposite ]
Probability[ something ]
=1 - Probability[ opposite ]

Random drawing with replacement
– after each draw, the ticket selected is
placed back into the box

Random drawing without
replacement
– after each draw, the ticket selected is
not placed back into the box
Conditional Probability
The probability that something will happen
given the information that a first thing has in
fact happened.
Notation:
“given”
Pr[ outcome 2 | outcome 1 ]
“The conditional probability that outcome 2
occurs given that outcome 1 has occurred.”
Conditional Probability
The probability that something will happen
given the information that a first thing has in
fact happened.
Drawing without replacement example:
Pr(2nd Red | 1st Red) = 1/5
Unconditional Probability
NOTE: The “standard” probability
without a condition is called the
unconditional probability.
Multiplication Rule
The Chance that two things will BOTH
happen equals the chance that the first
will happen, multiplied by the chance
that the second will happen given that
the first has happened. (Text, p. 229)
Pr[ first AND second ]=Pr[ first ] x Pr[second | first ]
Careful !! -- Multiply probabilities and convert
to chance