Basic Probability

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PRESENTATION OUTLINE

BASIC PROBABILITY

CHAPTER 5
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SCHLITZ BREWING COMPANY - 1981

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BINOMIAL EXPERIMENT

AKA, BERNOULLI TRIAL
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“INDEPENDENT”

ONE CASE DOESN’T AFFECT ANOTHER
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98% chance that at least 40 would pick Schlitz

86% chance that at least 45 would pick Schlitz

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The odds that no one picked Schlitz:
1 in 1,267,650,600,228,229, 401,496,703,205,376

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PROBABILITY IS POWERFUL

THE POINT
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Probability:

The study of events and outcomes involving an element of uncertainty

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LOTS OF STUFF HAS KNOWN PROBABILITIES

EX: TRAVEL AROUND AUSTRALIA

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EX: NASA’S SATELLITE, 2011

Probabilities do NOT tell us what will happen. They tell us what is more or less likely to happen.

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FEARS DO NOT ALWAYS FOLLOW THE ODDS

PROBABILITY AFTER THE FACT

WHAT LIKELY HAPPENED?
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DNA ANALYSIS: 99% OF DNA IS IDENTICAL

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Untitled Slide

  • Anything less than a full match leaves room for uncertainty
  • The more loci tested, the less uncertainty
  • Context matters
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13 LOCI

PROBABILITIES BASED ON ESTIMATES
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PROBABILITY OF TWO EVENTS BOTH HAPPENING

PRODUCT OF THEIR RESPECTIVE PROBABILITIES (MULTIPLY)
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PASSWORDS

“INDEPENDENT”

YES, AGAIN
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PROBABILITY OF ONE OR THE OTHER HAPPENING

SUM OF THEIR PROBABILITIES (ADDITION)
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“INDEPENDENT”

I JUST CAN’T TIRED OF SAYING THIS...
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What are the odds of getting one of two events that are NOT mutually exclusive (a king or an ♠️)?
The sum of their individual probabilities minus the probability of getting both

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EXPECTED VALUE

SUM OF ALL THE DIFFERENT OUTCOMES WEIGHTED
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THE POINT AFTER

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THE LOTTERY

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“LAW OF LARGE NUMBERS”

OR WHY CASINOS ALWAYS MAKE MONEY
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PROBABILITY DENSITY FUNCTIONS

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INSURANCE

TRANSFERRING RISK FOR A REGULAR PAYMENT
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“EXPECTED LOSS”

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Insurance that is for-profit will not save you money in the long run, so only take insurance to protect against risks you cannot afford

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DECISION TREES

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INVESTMENTS

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WIDESPREAD SCREENING FOR RARE DISEASES

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USING PROBABILITY

TO CATCH INSIDER TRADING - THE SEC
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SANTA CRUZ & CHICAGO: PREDICTIVE ANALYTICS

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AUTO INSURANCE: “HOT WHEELS” REPORT

CREDIT CARD COMPANIES

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PROBABILITY IS NOT DETERMINISTIC

LIKELIHOOD, NOT DESTINY
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Leeda Copley

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