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
How to assign probabilities
near 0: unlikely
near 1: likely
near 1/2: may or may not occur (either equally likely)
Venn diagrams can help!
Personal approach: guess!
requires experience; often used when have no previous data
ex: estimating the probability a totally new aircraft design will crash
on its first flight
Relative frequency approach:
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
requires ability to repeat
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 =
- 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)
valid only if outcomes are equally likely!
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.