Difference between revisions of "What's on Back POW"

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<big>'''[[IAG 1H]] POW <nowiki>#</nowiki> 5: What's on Back?'''</big>
 
<big>'''[[IAG 1H]] POW <nowiki>#</nowiki> 5: What's on Back?'''</big>
  
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==Problem Statement==
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{{IMP Takedown}}
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Not necessary to do.
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==Process==
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I started out on this POW thinking that you have a fifty-fifty chance all of the time.  This was not true.
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As I started making my bag, a few “cheap” strategies came into my head.  I figured I could make corners.  I could recognize how many X’s were on the sides which were lined.  (I ended up using unlined cards.  Finally, I realized that you could recognize imperfections of the way in which you write the letters.  Next, I figured out that the front and back are interchangeable. 
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I started working getting trials by picking cards out of a bag.  I didn’t have any specific strategy, I was just pulling cards.  I recorded the pulls as follows: The front; what I thought was on the back; Correct (1) or not (0).  I was correct 9/16 times.
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I then started trying to use a strategy.  I tried guessing the same.  I was correct 8/10 times in that section.  Overall, when I guessed the same, I was correct 17/23 times.  To find the theoretical probity, I drew 3 cards, an X X O.  I then flipped them over, on the other side respectfully was a X O O.  2 out of 3 were the same.  I then shook the bag around and picked 3 more cards: X O O.  On back were: X O X. 2 out of 3 were the same again.  Therefore, I can conclude that guessing the same gives you a 2/3 chance of being correct.  I can also conclude that picking different gives you a 1/3 chance of being correct, because it is the opposite of choosing the same.
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I then tried another strategy, picking always X.  In that section I was correct 6/11 times, which is also very close to half.  Then, to find the theoretical probity, I picked 3 cards again: O X X, and on the back was O X O.  If I picked X, I would have 1/3.  I picked 3 cards again: O X O.  On the back was: O X X.  If I picked X, I would have 3/6 or ½ chance of being right.  This means that always picking X gives you a fifty- fifty chance of being right.  I suspect the same is true for always O.
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===Experiment===
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{|border="2" cellspacing="0" cellpadding="4"
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|<small>Front</small>
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|align = "center"|<small>Back ???</small>
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|align = "center"|<small>Correct</small>
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|align = "center"|&nbsp;
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|align = "center"|<small>Expermented----------------</small>
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|align = "center"|&nbsp;
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|-
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|align = "center"|<small>X</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|-
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|-
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>X</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|&nbsp;
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|align = "center"|<small>Guess Same---------------------------</small>
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|align = "center"|&nbsp;
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|-
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|-
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>O</small>
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|align = "center"|<small>O</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|&nbsp;
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|align = "center"|<small>Guessed X------------------</small>
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|align = "center"|&nbsp;
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|align = "center"|<small>O</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>O</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|align = "center"|<small>O</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|-
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>O</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#FF0000"><small>0</small></font>
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>O</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|align = "center"|<small>X</small>
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|align = "center"|<small>X</small>
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|align = "center"|<font color="#339966"><small>'''1'''</small></font>
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|}
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===Assistance===
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I pulled cards with Steven Marcus and Glen.  I also helped them understand the solution I came across.
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==Solution==
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I found that picking the same letter gives you a 2/3 chance of winning, which is what your strategy should be.
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==Extension==
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Not necessary to do.
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==Evaluation==
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Not necessary to do.
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[[Category:IAG 1H]]
 
[[Category:IAG 1H]]
 
[[Category:POW]]
 
[[Category:POW]]

Latest revision as of 16:19, 11 December 2008

IAG 1H POW # 5: What's on Back?

Nuvola apps important.png IMP Takedown

I was asked to take down POW solutions. Remember it's best to think about how to solve the problems on your own.

Retrieved from "https://wiki.theplaz.com/w/index.php?title=What%27s_on_Back_POW&oldid=11674"