I Do Not Believe It!

 It is quite a three-pipe problem and I beg that you won’t speak to me for fifty minutes.

Sherlock Holmes

I Can't believe it Sign

You are appearing live in a TV game show. The manic presenter shows you three boxes, labelled A, B and C. One of them contains a cheque made out to you for £1 million. The other two contain photos of the presenter. He knows which box contains the cheque, and that cheque will be yours if you pick the right box. You go for Box A. The presenter reaches for Box C and shows everyone that it contains one of the pictures of himself. The cheque must be in Box A or Box B. You picked Box A. The presenter now asks you if you want to stick with your original choice of Box A or switch to Box B. What should you do? Maybe you have an impulse that urges you to switch your choice to Box B, while another voice is saying, Stick with Box A; he’s just trying to make you switch to a less expensive option for his employers.’ Or perhaps a more rational voice is telling you that it can’t possibly make any difference because the cheque is still where it always was and you either guessed it right first time or you didn’t. The answer is remarkable. You should switch your choice to Box B! If you do this you will double your chance of picking the box that contains the cheque. Stick with the choice of Box A and you have a 1/3 chance of winning the cheque; switch to Box B and the chance increases to 2/3. How can this be? At first, there is a 1 in 3 chance that the cheque is in any box. That means a 1/3 chance that it’s in A and a 2/3 chance that it’s in B or C. When the presenter intervenes and picks a box, it doesn’t change these odds because he always picks a box that doesn’t contain the cheque. So after he opens Box C there is still a 1/3 chance that the cheque is in A but now there is a 2/3 chance that it is in B because it definitely isn’t in C. You should switch.

Girl write in board (B.I.Y.)

Still not convinced? Look at it another way. After the presenter opens Box C you have two options. You can stick with your choice of Box A and this will ensure you will win if your original choice was right. Or you can switch boxes, to B, in which case you will be a winner only if your original choice was wrong. Your first choice of Box A will be right 1/3 of the time and wrong 2/3 of the time. So changing your box will get the cheque 2/3 of the time while staying with your first choice will be a winning strategy only 1/3 of the time.

You should by now be convinced by this mind-changing experience.

Also Read:- Not Going with the Flow

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Image Credit :- Pixabay

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