Probability

1
Probability Risk andPerceptions of Randomness

• Plous Ch 12 Ch 14

2
Probability Risk

• Simple probability Whats P of event x?
• Conditional probability Whats P of
• event x if z happens?

3
What is simple probability? conditional
probability?

• Simple P of event x Conditional
• P of event x if z happens?
• how avoid bias?

• Use Bayes theorem or close attention prior P

4
Common bias confusion of the inverse

• Probability of a compound event
• I.e.. whats odd lump in breast malignant?
  (1/100)
• Xray accurate 80 malignant tumors
• 90 benign tumors
• Whats changes of malignancy from xray?
  (.80)(.01) / (.80)(.01) (.10)(.99)
• .075 or 7.5

5
If compound event

• Pay attention to prior probabilities

6
How to avoid bias?

• Pay close attention to
• PRIOR Probabilities
• P of negative or positive events on your life
• 15 more likely than peers to experience
  positive events

7
Probability valence

• positive outcomes viewed more probable than
  negative ones
• 70 smiling faces estimates 68

8
Negative valence

• frowning face Es frown only 57.5 trials (less
  70 of cards with frown)

9
2nd probability bias positive outcomes judged
more likely

• rate probability of outcome will occur
• which of 2 outcomes will occur
• bet on given outcome occurring

• If 70 cards smiling face.gtpredict 68 would be
  smiling
• If 70 cards frowning factgtpredict 57.7 would
  be frowning

10
What if its a prediction about yourself?

• Whats LIKELIHOOD you will experience positive
  events compared to other mids? (15 more likely
  compared to others)
• ...to experience negative effects? (20 less
  likely)
• (Weinstein, 1980)

11
Overestimate probability of compound
(conjunctive) events

• 2-stage lottery odds of a breakdown in a complex
  system
• ballistic missile-500
• subsystems. Whats chance it will work on lst
  attempt?
• p is less .01

12
Underestimate probability of disjunctive events

• Whats odds drawing 4 colored marbles in urn with
  10 colored 10 white?
• Whats odds of event x happening again once it
  occurs (machine failure limited nuclear war)

13
CONSERVATISM

• Once people form a probability estimate, they
  are often slow to change the estimate given NEW
  INFORMATION
• takes 2-5 observations to do one observations
  worth of work in inducing change of opinion
  (Edwards,196818)

14
Perception of Risk

• Smoking 1.4 cigarettes increases odds of death
  by same amount as living w/I 20 miles of nuke
  power plant for 150 years(Wilson,1979)
• So why do people continue to smoke?

15
Subjective nature of risk

• People more likely to accept voluntary risk

• 3 dimensions or types of RISKS
• (Slovic, 1987283)
• 1 dread risk - perceived loss of control
• 2 unknown risks - unobserved or delayed (gene
  splicing)
• 3 No. of people exposed to risk

16
Expert Vs Novice differences Risk Estimates

• LAY People
• Influenced by catastrophic potential and threat
  to future generations in estimating annual risks

• EXPERTS
• Better job at estimating annual risks
• I.e.. Risk of nuclear power

17
Do accidents make us safer?(reactions to near
missesgtreinforces prior attitudes)

• After false alarm that caused 100 B-52 to go on
  high alert
• Most opponents of nuclear deterrence reported
  feeling LESS SAFE
• Most supportersconfidence in system INCREASED

• Similar reactions Chernobyl nuclear accident.gt
• radiation fall-out from this accident
• 1 factors fueling democracy movement in C. E.
  Europe

18
RECOMMENDATIONS - for better risk analysis

• Maintain accurate records
• Beware of wishful thinking
• Breakdown Compound Events into Simple Events (.5
  .5 .5 .125)
• Be aware that feedback information will be most
  likely used to reinforce your prior beliefs

19
Perceptions of randomness

• unlikely coincidences
• Carl Jung synchronicity
• devine intervention

20
Can people recognize random series?

• Not really
• Es judged series with
• .40 probability of repetion as
• most random

21
Do people see meaningful patterns in random
series?

• YES

22
Can people behave randomly?

• Not easily
• Can be trained to act randomly across
• extended trials

23
Political implications???

• Politicans can claim
• credit for lots of
• things
• NEITHER party
• influenced!