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FSU - PHI 2100 - PHI 2100 Week 6 Notes - Class Notes

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FSU - PHI 2100 - PHI 2100 Week 6 Notes - Class Notes

School: Florida State University
Department: Philosophy
Course: Reasoning and Critical Thinking
Professor: Michael Bishop
Term: Summer 2015
Tags: philosophy, Probability, reasoning, criticalthinking, and logic
Name: PHI 2100 Week 6 Notes
Description: Mostly covers probability.
Uploaded: 10/27/2017
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background image October 16, 2016 Probability Ways of Talking Informal/common vs. precise Precise ways of using language Percentage- There is a 70% chance of rain.
Fraction- The probability is 7/10 that it will rain.
Normalized Scale- Runs from 0 to 1. There is a 0.7 probability that it 
will rain. A priori probability          A priori- prior to experience. What is the probability of drawing an ace from a standard deck of  playing cards? 4/52 or 1/13 Rules of Probability Rule 1: Negation- The probability that an event will not occur is one minus 
the probability that it will occur.
Pr(~h) = 1-Pr(h) What’s the probability of not drawing an ace?  13/13 - 1/13 = 12/13 Rule 2: Conjunction- The probability of two independent events is the 
product of their individual probabilities. 
Pr(h1 & h2) = Pr(h1) * Pr(h2)
background image The probability of drawing an ace, replacing it, and then drawing an  ace again is 1/13 * 1/13 = 1/169 Independence- Two events are independent when the occurrence of 
one does not influence to probability of the occurrence of the other.
Dependent- If we draw an ace, reshuffle without replacing it, and then
draw another ace, then the events are dependent. 
What is the probability of drawing the second ace? 1/13* 3/51 = 1/221 To extend rule 2 to dependent events, we needs to address conditional  probability. Conditional Probability- the probability of one event occurring given
that another has occurred
The probability of h2 given that h1 is called the conditional probability 
of h2 on h1 and is symbolized Pr(h2|h1)
Rule 2G: Conjunction in general: Given two events the probability of 
their both occurring is the probability of the first occurring times the 
probability of the second, given that the first has occurred.
Pr(h1 & h2) = Pr(h1) * Pr(h2|h1) Note that when h1 and h2 are independent, Rule 2G reduced to Rule 2. Rule 3: Disjunction  Disjunction with exclusivity: the probability that at least one of two 
mutually exclusive events will occur is the sum of probabilities that 
each of them will occur. 
Symbolically, where h1 and h2 are mutually exclusive Pr(h1 v h2) = Pr(h1) + Pr(h2)

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School: Florida State University
Department: Philosophy
Course: Reasoning and Critical Thinking
Professor: Michael Bishop
Term: Summer 2015
Tags: philosophy, Probability, reasoning, criticalthinking, and logic
Name: PHI 2100 Week 6 Notes
Description: Mostly covers probability.
Uploaded: 10/27/2017
5 Pages 38 Views 30 Unlocks
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  • 24/7 Homework help
  • Notes, Study Guides, Flashcards + More!
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