# Plep's Puzzles

Name:

## Saturday, September 25, 2004

### 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?

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!

tom said...

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

September 26, 2004 at 1:27 PM
Sean said...

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.

September 26, 2004 at 5:34 PM
steven said...

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.

September 27, 2004 at 3:35 AM
Anonymous said...

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

September 27, 2004 at 3:36 AM
Sean said...

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.

September 27, 2004 at 12:35 PM
steven said...

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.

September 28, 2004 at 1:39 AM