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Lecture 4

PSYB07H3 Lecture Notes - Lecture 4: Conditional Probability, Mutual Exclusivity, Odds Ratio


Department
Psychology
Course Code
PSYB07H3
Professor
Dwayne Pare
Lecture
4

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PSYB07: Probability
Odds ratio
Probability percentage
Probability: likelihood of some event happening
Event: occurrence of something
Notation: p(Event)
Basic Concepts
Probability is usually expressed in proportions
o 0-1
o Convert to percentage 0% - 100%
  pevet  
o p(event) = 0
o p(event) = 0.5
o p(event) = 1
Subjective view
o Based on personal judgment
Empirical view
o Based on the long run frequency
Analytical view
o Based on a mathematical model
Subjective View
Subjective judgment about the likelihood of an event
o Chance of rain tomorrow
o Probability of Toronto Blue Jays winning the World Series
o Chance that you would go out with the person you met at a party last week
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Empirical View
Toss a oi… reord the outoes
o 10 times: 7 heads 0.7
o 20 times: 12 heads 0.6
o 100 times: 55 heads 0.5
o 1000 times: 520 heads 0.52
o p(Head) = 0.5
Analytical View
Two possible outcomes Head, Tail
Event outcome Head
p(Head) = 1/2 = 0.5
Exhaustive events
Probability of rolling a  OR  OR  OR  OR  OR 
p(1 or 2 or 3 or 4 or 5 or 6)
= p(1) + p(2) + p(3) + p(4) + p(5) + p(6)
= 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6
= 6/6
= 1
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Exhaustive: Include all the possible outcomes
Probability of rolling a ≥
p4
= p(4) + p(5) + p(6)
= 1/6 + 1/6 + 1/6
= 3/6
= 0.5
Not exhaustive
Mutually exclusive events
Proaility of rollig a 4 OR a Odd uer
p4 or Odd
= p4 + pOdd
= 3/6 + 3/6
= 6/6
= 1
4 OR Odd
o 4 {4, 5, 6}
o Odd {1, 3, 5}
o 5 & 5 over lap
o Overlapping Not Mutually Exclusive
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