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The Monty Hall Problem
30404 Na Eun30416 Bora30419 Arthur30429 Jay
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Outline
Member 1 reason , Why is it useful & when can youuse it?
Member 4 show problem & video
Member 2 solve this problem with 2 ways
Member 3 - Give the class a problem to try, then showthe solution
Member 5 The Mastery
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Member 1 - reason , Why is it useful &when can you
use it?
- To learn more about possibility in whichwe use without being aware that weare using it, and are only aware of itwhen solving math problems
- Possibility is Always(emphasized)always used in our daily lives
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Member 4 - show problem &video
9822D7AE024021C&outKey=V1274295440a3732be766d96732a009e527a99a4fa21da01
http://serviceapi.nmv.naver.com/flash/NFPlayer.swf?vid=A030828FD94A3E6405AAB9822D7AE024021C&outKey=V1274295440a3732be766d96732a009e527a99a4fa21da0104c6bd96732a009e527a9http://serviceapi.nmv.naver.com/flash/NFPlayer.swf?vid=A030828FD94A3E6405AAB9822D7AE024021C&outKey=V1274295440a3732be766d96732a009e527a99a4fa21da0104c6bd96732a009e527a9http://serviceapi.nmv.naver.com/flash/NFPlayer.swf?vid=A030828FD94A3E6405AAB9822D7AE024021C&outKey=V1274295440a3732be766d96732a009e527a99a4fa21da0104c6bd96732a009e527a97/31/2019 Math Presentation2
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Member 2 Explain &solve the
problem
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Member 2 Explain &solve the
problem
We can solve this problem with 2 ways
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Number 1 : Graph
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Number 2 - Formula
We can determine these probabilities using the rule
In words: The probability of event A given event B is theprobability of both A and B divided by the probability of B.
( )( )
( )Bp
BApBAp
=|
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In the following argument :
Assume that:
-we originally chose door #1.
-Monty opened door #2.
Notation
-Let #1 denote the event that the prize is behind door #1, and
similarly for doors #2 and #3.
-Let opened #2 denote the event that Monty has opened door #2.
Our aim is to compute p(#1 | opened #2) and p(#3 | opened #2).
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( )( )2#opened
)2#opened1(#2#opened|1#
p
pp
=
( )( )
( )
( ) ( ) ( )BApBpBAp
Bp
BApBAp
|2.
|1.
:Rules
=
=
( )( )
( )2#opened
2#opened3#2#opened|3#
p
pp
=
(If the prize is behind door #1, Montycan open either #2 or #3.)
(If the prize is behind door #3, Montymust open door #2.)3
1
3
11 ==
6
1
3
1
2
1==
( ) ( ) ( )1#1|#2#opened2#opened1# ppp = (By rule 2.)
( ) ( ) ( )3#3|#2#opened2#opened3# ppp = (By rule 2.)
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( )( ) ( )2#opened
6/1
2#opened
)2#opened1(#2#opened|1#
pp
pp =
=
( ) ( )( ) ( )2#opened
3/12#opened
2#opened3#2#opened|3#pp
pp ==
( ) ( ) ( ) ( )
2
1
3
106
1
3#2#opened2#2#opened1#2#opened2#opened
=++=
++= pppp
So:
( )3
2
2/1
3/12#opened|3# ==pand( )
3
1
2/1
6/12#opened|1# ==p
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Conclusions
Switching increases your chances of winning to 2/3.
A similar result holds for n doors.
This strategy works only if we assume that Monty behaves
predictably, offering a chance to switch every time.
On Lets Make a Deal, Monty would play mind games withcontestants, sometimes offering them money not to open the
selected door.
Play the game and check out the statistics athttp://math.ucsd.edu/~crypto/Monty/monty.html
Lets Make a Dealgraphics courtesy of letsmakeadeal.com
http://math.ucsd.edu/~crypto/Monty/monty.htmlhttp://math.ucsd.edu/~crypto/Monty/monty.html7/31/2019 Math Presentation2
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Member 3 another problemThere are 3 prisoners. 1 prisoner will get a death
penalty, and the remaining 2 will be released from jail.However, they do not know who will be released or bekilled. Here, the possibility of one person getting a
death penalty will be 1/3.
One prisoner asked the guard, "Among the 2 prisoners
other than me, who will be released tomorrow?" Since 2among 3 prisoners will be released, at least 1 among
the remaining 2 will be released. That is, other than theprisoner who questioned the guard.
Then the guard refused to tell the prisoner. "If I tell it toyou, the possibility of you getting a death penalty willbecome higher." Was the guard's explanation
reasonable? Explain your answer regarding the math ofpossibility and in a logical way.
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Lets solve this problem
ANSWER IS
Guard`s explanation is inappropriate
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Member 5 The Mastery
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Thank you