Class notes

Probability and Decision Analytics

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Course
MGSC 660

Institution
McGill University (Mcgillu)

These notes provide a detailed introduction to probability, It covers conditional probability, joint probability, solving probabilities through multiplication and addition rules. with examples. It also covers decision trees, both one stage decision trees and multi staged decision trees, with exampl...

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Uploaded on August 1, 2024
Number of pages 36
Written in 2024/2025
Type Class notes
Professor(s) Mehmet gumus
Contains All classes

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, Basics
Probability

>
-
probability :

>
-
Likelihood or chance that a particular event will occur -

> is
proportion fraction whose value from O to
I
a or
ranges
-

↳ an event that has no chance of
occurring has a
probability of
o

↳ while an event that is sure to occur has
probability of 1

about information the
probability of event
might differ
probability
>
-

. an
is

available into that
from person to person based on the
they have
↳ that events will into
the
probability occur
may change as -
accrues

or evolves
.

3 Bask components of
probability theorem :

Experiment

2) Elementary outcome

3) sample space (S)

1) Experiment
>
-

any process that produces a
single outcome whose result cannot be

predicted with
certainty
.

i) rolling a die

card draw
ii) A 3 .

,2) Elementary outcomes

outcome of experiment
unique
> a an
-

2
elementary outcomes
mutually exclusive
>
are
-

i) rolling 3 die loss
a in a
single

ii) picking an ace of spades
.

Event
3)
set of of interest
>
elementary outcomes
-

I) one or more heads in a 2 coin toss

ii) the sum of dices is greater than 7
.

7) sample space (s)

>
-
set of all possible elementary outcomes of an experiment

(Mutually exclusive and collectively exhaustive) .

consists of from a box
Example : an experiment drawing one marble

of
that contains a mixture red , yellow and green marbles

>
-

sample space-s = [red ,
yellow ,
green 3
↳ unique color combinations
.

, suppose you are
only interested in the no , of red marbles drawn :

S = 20 .
13

↓ Y
of
outcomes
drawing
outcomes of
red
.

drawing yellow
and
green

R 72

R OR RY RG

YR Y +G
Y

GR GY GG
E

i) S :
Err , ry , ug ,
yr , yy ,
yg ,
gr , gy , gg
3

ii) S = 30 ,
1
,
23

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