nomena are not involved. In the case of
modeling, stochastic models are based on
random trials, while deterministic mod-
els always produce the same output for a
given starting condition.
Are “random” numbers generated
by a computertruly random?
For most general purposes, random num-
bers generated by a computer can be con-
sidered “random.” But in reality, because
a computer follows a set of rules in any
program, the numbers generated are not
truly random. In order for a sequence or
specific numbers to be truly random, they
must not follow any sort of rules. That’s
something to think about the next time
you purchase a computer-generated, “ran-
dom-numbers” lottery ticket.
What is the concept of relative frequency?
Relative frequency is actually another term for proportion. It can be found by dividing
the number of times an event occurs by the total number of times the experiment is
done. In probability, this is often written in the notation rfn(E) r/n, in which Eis
the event, nis the number of times the experiment is repeated, and ris the number of
times Eoccurs. For example, a symmetrical coin can be tossed 50 times (n) in order to
find out how many times tails will occur (E). If the result is 20 tails (r) and 30 heads,
then the equation becomes 20/50, or 2/5 0.4; or, the relative frequency is 0.4 for
tails. If this experiment is repeated over and over, the relative frequency will eventual-
ly get closer and closer to 0.5, which is the true value that should result when tossing
a two-sided symmetrical coin.
How are the terms outcome, sample space,and eventrelated?
These terms are definitely related: The outcomeis the result of an experiment or other
type of situation involving uncertainty; and the set of all possible outcomes is a sample
space. Just as important are events,which are collections of the outcomes of an exper-
iment, or any subset of the sample space. If there is only one single outcome in the
sample space, it is called an elementary or simple event; events with more than one
outcome are called compound events. 249
APPLIED MATHEMATICS
Gamblers who play the lottery are well acquainted
with the concepts of random numbers and probabili-
ty. The Image Bank/Getty Images.