1-1
Objectives
Introduce students to the basic
concepts of probability, including:
 randomness
 combined probability
 dependent events
 independent events
 gambler’s fallacy
1-2
Defining Probability
Probability is
A. the likelihood that a given
will occur
B.
A number expressing the
likelihood that a specific
event will occur, expressed
as the ratio of the number
actual occurrences to the
number of possible
occurrences (Soukhanov, 1992)
event
of
1-3
Probability of
rolling a “1”
(# of favorable results)  (# of
possible results) = 1/6
A "favorable result" is the
result for which you are
determining the probability. In
this case, you are determining
the probability of a single event
1/6 = .17 = 17%
1-4
Randomness


Each possible outcome in that
process has the same chance, or
probability, of occurring
Outcomes are determined by chance
1-5
Probability in the
Real World
Probability = # Favorable Outcomes
Total # Trials
Probabilities based on trials are
an estimate
1-6
Combined Probability
Probability of the 1st event AND
2nd event occurring
Probability of 1st event
X
Probability of 2nd event
Combined Probability
1-7
Is an Event Dependent
or Independent?
INDEPENDENT
The outcome of the 1st event
does not affect the outcome
of the 2nd event
DEPENDENT
The outcome of the 1st event
does affect the outcome of
the 2nd event
1-8
Gambler’s Fallacy
Mistaking independent
events for dependent
events
In reality, the outcomes are
completely independent
1-9
Probability of One Event
vs. a Group of Events
Assumption: Outcome is
Random
Probability of 1st x 2nd x 3rd
x 4th =
Combined Probability of a
group of events
1-10
Shared Birthdays
With any group of 23 people, there
is a 50% chance that two or more
people in that group will have the
same birthday
1-11
Heads or Tails?
In your group, flip the coin
20 times
Each group will record the
results


count the number of heads and tails
calculate the percentage
of heads
1-12
Outcome and
Probability
What are all the possible
outcomes for flipping two coins?
 heads/heads
 heads/tails
 tails/heads
 tails/tails
What are the probabilities of
each outcome?
1-13
Becoming a Legend
Batting Average calculated
# Hits during season
Total # times at bat
.400 batting avg. means
a hit 4 out of 10 times
at bat
1941: Ted Williams
approached the last day of
play with a .39955 (179/448)
The Red Sox coach offered to let Williams sit out the last day
to avoid slipping below .400
1-14
Becoming a Legend:
Part II



Given Ted Williams batting average before the
last day (.39955), how many hits would you
expect him to get out of 8 times at bat?
If Williams went to bat 8 times on his final
day and got the number of hits calculated
above, what would his season average have
been?
Would you have played the last games or sat
them out?