MATH 1711 GIT Probability Finite Math Questions

Week 5
1711:
Lecture Notes
I
A
H
Example
Usually refer
the prob
to
ppleat
1000
e.g.
statistics)
(Heath
39 out
of those
How
do
->
we
the
1.75
ounces
eating
choc
had
of absolute
risk reduction
–
39
5
=
=
the method of relative risk
reduction
risk
50
–
39
=
the number
to
needed
in
participate
treat
to
the
and
1000
50 out
ofthose not
would
not
eating
eating,
reportthat:
1.1%
=
reduction
would report
that:
1 22%
=
50
->
stroke, and
a
reduction
1000
->
risk.
eating chocolate?
risk
50
or
of chocolate per week,
benefit of
report, the
method
chance
as
=
method
treatment in
would
order
to
reportthat
the number
preventas stroke
is
of ppl
needed
10,00:al ppl
not to be confused
Last time
#
we
saw
the
rule:PIENF) PIEIE). I(F)
product
with
=
T
is
second set
This
I
can
be
generalized
by applying the
as:
IP(ANBNC)
productrule twice)
PCA) IPCBIA) IIC Inn)
independency
IP (ANB) B(A). D(B)
=
repeated
Example
I
Roll
red
~>
a
Example
&
a
I roll
the
What
is the prob
and
geta
red
one
fair
blue
and
that
as
Pick
b-sided die
geta
I roll
Pick
4.
I
the blue
IP(b(ve 3) 1/6
=
=
Not affected
prob of that
IP(first
Now
pick the
let’s
P
but
have
multiple
=
(second red)
=
prob
->
be
&
is
IP(first-blue) =10/20
10 blue
red) 10120
=
second ball
=
The
can
10 red
own
IP(second:blue) 9/19
by the firstroll
Independency
with
an
ball
Similarly,
events!
Independent
->
balls out of
blue
a
the
one
3?
2
2
1
PIE, n Ec
generalized
conditions:
n
9/19
=
changes!
dependentevents.
Es) B(E). IP(Ez). PCES)
=
IP(E,nEz)
1P(E). IIEz)
=
IP(E,nE3) P(E). IP(E3)
=
P(EzME3) P(Ez)
½
I(Es)
?6.5Tree Diagrams
are
used
I recall
as
a
visual
for example
Process:
“make scrambled
representation
the
of
multiplication
3
sequential
principle
choices
where
we
“break”our
process into
a
series
of
smaller
steps)
Decomposition:
eggs puta pan on
the stove turn it
on
go
to the
fridge
–
geteggs
& butter
etc.
Example Polling in two major Pennsylvania
Technique:Select
In
Philly 25
city randomly & poll
a
&
Ropublican
are
choose
city
?
a
Republican
218
->
1
Democrat->
Republican
A
Pittsburgh
->
?
113
probs of
&
I.E =
in
the
7
I.E =
5
->
Democrat
probs of picking
Republican
are
->
?
picking cities
Pittsburgh
voter
random
Pittsburgh
in
At
t Philly
a
cities:Philadelphia
=
I.z 5
=
D vs R
multiply everything
together
prob of intersection
=
city
(i.e. conditional prob
So
we
can
PC Pitts
?
find:
n
Dem) IP(Pits).
=
P(Dem
.
IPits) I
z
=
(Repob) IP (Repob n Pitts) IP(Repub
=
+
1/5
=
P (Philly/Repub)
1/3
+
8/15
n
5
=
Philly)
Republican
Philly
=
IP (Philly
n
Republ
=
P (Republ
1/5
3/8.
=
=
8/15
Some
&
Pitts
live in
some
in
Pitts
Philly.
Week 6
1711:
Lecture Notes
I
A
H
Defin
The
of getting
a
sensitivity of
The
specificity
The
positive predictive
The
negative predictive value
56.6
the
Bayes’
Example
prob
procedure/testis
medical
result
when
positive
is
a
of getting
(PPU)
value
(NPV)
is
has
the person
a
the
prob of
prob
of
not
prob
Out
of the
the person
having the
ppl
that
given a positive result
condition
given a negative result
having the
test
positive
test
2%
negative
test negative
99%
98%
TB
have
ppl that don’t have TB
2
of
them
have
tests
0.8002
pick
P
->
IP(TBN p)
0.000196
=
TB
N
0.02
person
->
I (TBnN)
0.000004
=
Iconditional
?
°ositive
TB.
0.98
a
has the condition.
condition
1%
10Kppl,
0214/23
Theorem
Out
of the
Per
Tuesday
condition.
result when
negative
is the
the
the
9
998
0.01
TB’
p
N
0.99
->
->
P
(TB’n p) 0.00998
=
P(TB’n N) 0.98982
=
What
is
the
prob that
D(P) D(PNTB)
p