Probability
Probability
– the measure of the likelihood of a random event
Probability Experiment
– repeatable process that produces uncertain results
Tossing two dice,
flipping a coin twice,
drawing five cards from a deck, …
Outcome
– result of a probability experiment
7,
HT,
KH, JD, 3C, 7H, 10S, …
Law of Large Numbers
– as the number of repetitions of a probability experiment
increases, the empirical probability approaches the theoretical probability.
Sample Space
– set of all possible outcomes of a probability experiment
1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
HH, HT, TH, TT
too many to list …
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
Event
– any collection of outcomes from a probability experiment
7 or 11
at least one T
All diamonds …
Classical (Theoretical) Probability
– probability measurement based on
(number of ways an event can occur) / (number of possible outcomes)
8
36
=
2
9
3
4
1287
2598960
…
Empirical (Statistical) Probability
– probability measurement based on
(number of observed events) / (number of experiment trials)
4 seven or elevens thrown
four our of four times
out of five hands dealt, none
out of 36 tries.
at least one tail was thrown
had all diamonds …
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 Spring '14
 Probability, Probability theory, 48 52

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