1 Introduction to Probability and Counting
1.1 Heuristic Probabilities
Idea: Assign value between 0 and 1 to event; magnitude gives likelihood
event will occur
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near 0: unlikely
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near 1: likely
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near 1/2: may or may not occur (either equally likely)
How to assign probabilities
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Personal approach: guess!
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requires experience; often used when have no previous data
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ex: estimating the probability a totally new aircraft design will crash
on its first flight
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Relative frequency approach:
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conduct experiment many times; then
P = m/n, where
n = total number of times
experiment is conducted
m = number of times in which
desired phenomenon occurs
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requires ability to repeat
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ex: weather forecast
If it rains on 15 out of 50 days with identical meteorological conditions,
then the probability of precipitation for a day with those conditions is
P = 15/50 = .30 =
30%.
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Classical Approach:
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- compute total number of possible outcomes, n(S)
- compute number of outcomes with desired result A, n(A)
- then probability P = n(A)/n(S)
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valid only if outcomes are equally likely!
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ex: roll 1 die; what's probability get an even number?
n(S) = number of possible values = 6
n(A) = number of values with desired property (even) = 3
probability P = n(A)/n(S) = 3/6 = 1/2.
Venn diagrams can help!
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