STAT 1301

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STAT 1301

• Introduction to Probability

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• Statistics
• The Science of Decision Making in the Face of
  Uncertainty
• Uncertainty makes life challenging and
  interesting
• very few things are absolutely certain

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• Chance Situations
• Flip coin -- What is the chance of heads?
• What is the chance that SMUs 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.

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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
• Chanceoutcome x 100

X
N
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Drop Thumbtack
Chance it lands point down ?
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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.

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3 Ways to Calculate Chance

• (3) Subjective (Degree of Belief)

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Virtual Impossibility Virtual
Certainty
Facts About Chance
Probability is chance expressed as a fraction

• Chance 0 Chance
  100
• Probability 0
  Probability 1

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• Chance outcome does not occur
• 100- Chance outcome does occur
• IN GENERAL
• Chance something
• 100 - Chance opposite
• Probability something
• 1 - Probability opposite

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• 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

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Conditional Probability The probability that
something will happen given the information that
a first thing has in fact happened.

• Notation
• Pr outcome 2 outcome 1
• The conditional probability that outcome 2
  occurs given that outcome 1 has occurred.

given
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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
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Unconditional Probability

• NOTE The standard probability without a
  condition is called the unconditional probability.

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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 Prsecond
  first
• Careful !! -- Multiply probabilities and convert
  to chance