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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=V1274295440a3732be766d96732a009e527a99a4fa21da0104c6bd96732a009e527a9
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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.html
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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