1-1 Objectives

1
1-1Objectives

• Introduce students to the basic
• concepts of probability, including
• randomness
• combined probability
• dependent events
• independent events
• gamblers fallacy

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1-2Defining Probability
Probability is A. the likelihood that a given
event will occur B. A number expressing the
likelihood that a specific event will
occur, expressed as the ratio of the number
of actual occurrences to the number of
possible occurrences (Soukhanov, 1992)
3
1-3Probability 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
4
1-4Randomness

• Each possible outcome in that process has the
  same chance, or probability, of occurring
• Outcomes are determined by chance

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1-5Probability in the Real World
Probability Favorable Outcomes Total
Trials Probabilities based on trials are an
estimate
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1-6Combined Probability
Probability of the 1st event AND 2nd event
occurring Probability of 1st event
X Probability of 2nd event Combined Probability
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1-7Is 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
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1-8Gamblers Fallacy
Mistaking independent events for dependent
events In reality, the outcomes are completely
independent
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1-9Probability 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
10
1-10Shared 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
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1-11Heads 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

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1-12Outcome 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?

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1-13Becoming 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

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1-14Becoming 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?