ITI 111
Mor Naaman, PhD
and
Paul Kantor
Probability Notes
03 Probability
1. Probability
1.1.
Probability Intro and Motivation
Wikipedia
:
A way of expressing knowledge or belief that an event will occur or has
occurred
―
If a fair coin is tossed, what is the prob
ability of getting heads?‖
―If
a fair coin is tossed 10 times
; what is the probability of getting 8 heads?‖
In order to clarify the relation between the actions and the things that happen
after those actions are taken, we are going to introduce one more term:
experiment.
This does not mean quite the same thing as an experiment in a
chemistry lab. It is a technical way of referring to the action that has a
random outcome.
Outcomes, and Sample Spaces
—
An
experiment
governed by chance has several possible
outcomes
—
The collection of all possible
outcomes
in an experiment is the
sample
space
Example experiments:
—
Tossing a coin
—
Rolling a die
—
Rolling two dice
—Getting ten result pages for query ―sleeping baby‖
Example outcomes:
—
Heads
—
The first die shows a 4, and the second shows a 5
—
10 specific web pages (query results) in a specific order
Corresponding Sample Spaces:
{Heads, Tails}
 All possible combinations of two die {(1,1), (1,2), (2,1), (1,3),
(3,1),…(6,6)}
 All possible set of 10 different web pages
1.1.1. Probabilities In Web Search
More details later, but a couple of examples on how we are going to use it:
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ITI 111
Mor Naaman, PhD
and
Paul Kantor
Probability Notes
03 Probability
* Estimates on how many result pages will be returned for each query
* The Probability that a user who entered a given query will be satisfied by a
specific document
E.g. for each particular page that it might deliver, what fraction of the users
will think "yes this is exactly what I want"? In this case we want to know
statistics about all of the users who might enter the query terms: flying,
lessons, Hawai‘i.
A third concept: the probability that a web page that has a particular set of
features (such as the words that are in it) will satisfy ―this particular user‖
who has just asked us a query. In this case we want to know more about the
particular user.
1.1.2. Outcomes and events
—
We will agree to use the general term
Event
=
to mean ―
a collection of
possible outcomes in an experiment
‖.
—
A die rolls 5 or higher
—
It will rain tomorrow
—
A student will be late today
—
A student will get a grade better than B
—
More than 15 students will get a B
—
7 or more web pages are relevant to the query
1.1.3. Elementary Events
Elementary events can be counted, and are not composed of more elementary
events.
If the ―event‖ ―getting an
even number from the set of Integers
10
E
{2, 4,
6, 8, 10} elementary?
No! Seeing an even numbers from
10
E
is not elementary events, because it
can happen in several different ways. The set containing nothing but 2,
is elementary.
You
can‘t break it down any further. So the
set containing the
number ―2‖ is elementary in the set of numbers.
But it is just one part of the
set
0
2
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 Fall '09
 Boros
 Probability theory, Paul Kantor, Mor Naaman

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