I have just launched a new experiment on magic – if you have 2 minutes it would be great if you could take part. Details here.
On Friday I set this puzzle….
You meet a nasty dog in a dark alley. The dog has a bag and the bag has a pebble in it. The pebble is either black or white. The dog then adds a white pebble and shakes up the bag. He then asks you to take a pebble from the bag without looking inside it. What are your chances of taking out a white pebble?
If you have not tried to solve it, have a go now. For everyone else, the answer is after the break.
UPDATE: Having thought about this further, and had over 50 emails about the topic, I am of the opinion that the original answer is wrong. Sorry about that and thanks to everyone for pointing out the correct solution!
There are 3 possible scenarios:
1) The initial pebble was white. Thus both of them in the bag are white and so you will be left with a white pebble.
2) The initial pebble was black. Thus there is one white and one black pebble, and you remove a white pebble.
3) The initial pebble was black. Thus there is one white and one black pebble, and you remove a black pebble.
Thus there is a 2/3 chance of getting a white pebble.
Actual answer: .75 (see below)!
I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.