Tuesday, 10 January 2012

The Quiz Show Dilemma

By Lee Jaundrell 10/01/12

Picture the scene, you have just got through to the final round of a major quiz show, and you now have the chance to win £1million. To win this prize you have the choice of 3 boxes, in 1 box is the £1million, in the other 2 boxes is a dusty bin and a blankety blank cheque book and pen. Now choose your box; 1, 2 or 3.

After making your choice, Terry Monkhouse (the host) then takes away one of the other boxes saying the million pounds is not in it that one, and then offers you the chance to change your mind on which box you want. For example, you originally choose box 1, the host then takes away box 3. Do you keep box 1 or change to box 2?

What would you do?

I'm guessing you would probably stick to your original choice, but I would suggest 100% that you should always swap for the other box. And here's why;-

When you have the choice of 3 boxes, there is a 33.33% chance of the money being in any box, or in betting terms each box is a 2/1 chance, so as the example goes you pick box number 1;-

Box 1 - 33.33% chance

The host takes away box 3, leaving the chances of the money in each box as;-

Box 1 - 33.33%
Box 2 - 66.67%

Or in other words, it is odds on (1/2) that the money is in box 2, and a 2/1 chance of the money being in box 1. But, you will forever regret changing your mind if the money is in fact in box 1. That's the Quiz Show Dilemma.

What would YOU do? 

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