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WIN A CAR NOT GARBAGE

     

       We are going to analyze the TV game show. 'Let us make a deal".  There are three doors, A,B,and C.  A car is kept behind one of the doors and Garbage is kept behind others.  You are asked to choose one door behind which you think the car is present. Let us assume that you select the door 'A'.  Then, the anchor of the show open one of the other two doors where garbage is present.  Assume that he opens the door C.  Now the anchor asks you whether you want to switch to door B or stick to door A, because the car may be present in door A or B.  The C is already open.  Here the statistics says, better to switch to door B from A.  You will get more chance of winning the car".  Let us find out how? 

    In the beginning of the show, there are three closed doors.  If you choose one of them, you have 1/3 chance of winning the car.  When one door is open and you are allowed to change your door, you get 2/3 chance of winning the car.  If you stay with your original choice A, your chance also stays the same 1/3.  If you switch over to another door B, your chance of winning increases to 2/3.(2 times 1/3=2/3) 
If you toss a coin one time, the chance of winning a head is 1/2.  If you loss it 2 times, the chance is 2*1/2 =1.  One shows that there is certain win in two throws.  If you throw 10 times, the chance is 10*1/2 =5.  That is, you are likely to get head 5 times.  As the number of tosses increases, the winning chance also increases.  Similarly, if you go on choosing one door after another, your winning chance increases. 

    Let us look at the game show in another angle.  Suppose the show is performed 300 times in a year.  Each time the car is kept randomly behind one of the three doors.  In all the 300 shows, the participants initially choose door A (assume) and switches to another door later.  They are likely to win the car 200 times -2/3 chance.  If they do not switch over, they will only win 100 times -1/3 chance.  Here we are also assuming the game show is conducted honestly. 

FOOT NOTE:  The chance of winning is 1/6 means, out of 6 trials, you may win one time.  Out of 600 trials, you many win 100 times.  The moral of the story:  Even a dull candidate will win if he tries many, many times.     

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