1
Chapter 14 (From Randomness to Probability)
A roulette wheel contains 38 slots, 18 of which are red, 18 are black, and two are green.
If you were planning
to bet $5, what color should you bet on?
It’s impossible to know.
Assuming the game is fair, the outcome of
any one spin is completely unpredictable.
However, after many thousands of spins we see that the percentage
of times the ball lands in a red spot is a predictable number. This predictable value is called a
probability
.
(there’s an interesting example on page 365 regarding red versus green lights)
The study of
probability
is used to mathematically describe what we should expect to happen if an
experiment were repeated many times.
In effect, probability is used to describe
longterm behavior
(Law of
Large Numbers – see pages 366367 & graph on pg. 365).
It is the proportion of times a given outcome
occurs in many independently repeated trials
.
(See Jacob Bernoulli’s quote on page 367)
What is the probability of the roulette ball landing on red on any given spin?
P(red) =
What does it mean to say that spins of the roulette wheel are independent of each other?
A common mistake made when working with probability is to confuse the Law of Large Numbers
with the
Law of Averages
.
There is no such thing as a Law of Averages (it’s a fallacy – see pg. 367368).
An
interesting scenario about Keno and the Law of Averages is given on page 368 – these grad students “beat the
system” for $50,000 because the Keno game was not completely random (outcomes were predictable)
A quote from page 367:
Don’t let yourself think that there’s a Law of Averages that promises shortterm compensation for recent deviations
from expected behavior.
A belief in such a “Law” can lead to money lost in gambling and poor business decisions.
Activity 1:
Dr. Fidget developed a test to measure boredom tolerance.
He administered it to a group of 200 adults
between the ages of 25 and 35.
The possible scores were 0, 1, 2, 3, 4, 5, and 6, with 6 indicating the highest
tolerance for boredom (listen for 75 minutes without getting bored).
The results are shown below.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Ripol
 Statistics, Probability, Probability distribution, probability density function, Discrete probability distribution, Continuous probability distribution

Click to edit the document details