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...
>
-
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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