### Counters

A bag contains one counter, which has a 50/50 chance of being black or white. A white counter is put in, the bag shaken, and a counter drawn out, which proves to be white. What is now the chance of drawing a white counter?

Please comment on this post to propose an answer.

Answer in approximately one week.

NB :- I do enjoy puzzles, and I have written my own for a bit of fun on a MUD I used to frequent, but I'm far too busy/lazy to write my own for the purposes of this blog, which is intended as a bit of fun for regular readers of plep and anyone else who may happen by (though I may well recycle some of the puzzles I wrote all those years ago). I'm sure you could find the answer on the WWW with a bit of searching skill (this is an old puzzle - very old, in fact), but solving the puzzle by yourself is far more fun, believe me!

## 6 Comments:

I'll take a shot. If the first counter was white, the odds that the one left in the bag is white will be 100%

If the first counter was black, the odds are 0%

My guess is 50%

Tom

Okay,

the odds that the counter still in the bag is the black or white one is 50%. That counter has a 50% chance of being white. So 50% of 50% is 25%.

The odds that the counter is white are also 50%, but that counter would have a 100% chance of being white. So 100% of 50% is 50%.

50% and 25% is 75%.

At least, that's what my girlfriend says. I said 2. Two probability units.

I can say that you're both wrong. The answer is neither 50 % nor 75 %. Sean, 2 probability units out of how many ? (2/4, 2/3?)

Whilst it's not the same, I did find this puzzle after doing some research on the Monty Hall problem; so maybe taking a look at this will get you thinking along the same lines.

NB - I have now enabled anonymous commenting, sorry about that!

The two probability units was a joke. I'm not funny.

Okay - in my head I picture the first counter as being either black or white.... visually represented as black/white.

The second counter is white or...white. Visually represented as white/white.

So I have black/white and white/white. I pull out a white. That leaves me with black/white/white.

Odds are 2/3 that the next counter is white.

I'm just making this stuff up as I go along.

Sean, that's the right answer for the right reason (maybe my sense of humour wasn't working properly!).

This puzzle was from Lewis Carroll's 'Pillow Problems'.

I'll post another puzzle this coming weekend.

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