"We come
into the world and take our chances,
Fate is just the weight
of circumstances
That's the way that lady
luck dances,
Roll the bones"
- Rush
Chance as a deterministic
process
-
all supposedly random processes
can in principle be measured; if measured, would allow perfect prediction
nonetheless, probability
rules and concepts useful for describing patterns of events and dealing
with uncertainty
personal probability
relative frequency probability
Four key probability rules:
1) probabilities for all
possible outcomes in an uncertain situation must sum to 1
2) probability of one
or the other of two mutually exclusive events occurring is the sum of their
probabilities
3) if two events are independent,
probability of both occurring is product of their individual probabilities
4) if one event is a subset
of another event, probability of subset event cannot be larger than probability
of event for which it is a subset
expected value - average
value of an observation in the long run
sum of (probability of value
x value) across all possible values
Psychological effects on
reasoning about probability
certainty effect
availability heuristic
anchoring
representativeness
heuristic/conjunction fallacy
optimism
conservatism
overconfidence
Intuition and relative
frequency
people don't estimate relative
frequency probabilities very well in many circumstances
coincidences - common except
when you specify a particular event, time, context, & individual(s)
examples:
probability of a shared birthday
among 19 persons = 40%
-
BLS 315A estimates: mean
= 14.5%, median = 5%, mode = 0%
small world phenomenon -
"six degrees of separation"
Intel vs. AMD re "Am386"
chip
coincidences appear unlikely
because we fail to consider all noncoincidental events and experiences
gambler's fallacy/law
of small numbers - small samples represent the long-term pattern
-
if events are independent,
string of one outcome doesn't increase/decrease change that other outcome
will occur next
-
doesn't apply in cases where
events are not independent
confusion of the inverse
confusing probability of
having disease given positive test with probability of positive test given
disease
how likely is disease if
tested positive?
-
need three pieces of information:
1) base rate
of disease (prevalence)
2) sensitivity
- proportion with disease who test positive
3) specificity
- proportion without disease who test negative