Friday, 8 May 2009

Friday puzzle - Answered!

You're playing a game show and are offered a choice of three sealed boxes. One contains a cheque and will win you £100,000 and the other two are empty.

You pick a box at random.

Next, the host says he's going to make things more interesting by taking away an empty box. He opens one of the boxes you didn't pick and shows you that it's empty.

Now the host gives you a choice. You can stick with the box you chose originally, or swap to the other box that's still sealed. What should you do? Does it matter?

Answer next week! Don't give it away if you know.
(answer now below)


And the answer:

The first time I heard this puzzle, I swore blind it made no difference whether you switched or not - it does though and you should always switch boxes. Yes, even if as a colleague put it this morning 'you've got a really good feeling about the box you picked in the first place'... This isn't Deal or No Deal* and the colour of Noel Edmonds cardigan doesn't influence which box the prize is in.

Here's why.

When you first pick a box, you've got a 1 in 3 chance of having picked the right one and a 2 in 3 chance of having picked an empty one.

So, if you stick with the box you originally chose, your chances of winning are 1 in 3.

Now, lets assume you switch. If you had picked an empty box to start with and you switch, then you definitely win because the host has removed the other empty box.

There's a 2 in 3 chance that at the start you picked an empty box. So by switching, your chance of winning increases from 1 in 3 (you'd picked the right box first time) to 2 in 3 (you'd picked the wrong box first time and then switched to the right one.)

* Or as I heard a comedian call it once 'Let's Guess What's in the Box'

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