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?

As ever, please do NOT post your answers, but do say if you think you have solved it and how long it took.  Solution on Monday.

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.

1. Charles Sullivan says:

I think I got it. Not long at all, but it seems to simple to be true.

1. Charles Sullivan says:

too simple

2. Same here. I think I have it but it seems too simple.

2. Emlyn says:

Either this is very easy, or I’m missing something… Maybe the nasty dog hits you over the head with the bag of stones and steals everything you’ve got.

3. Tim says:

Have got waylaid worrying about the talking dog …

4. Hmmm I have an answer which is not the “obvious” answer. I think it’s right, but I’ll be interested to see on Monday. About a minute to put some things on paper and confirm.

5. I was beguiled by the “nasty talking dog” the probability of that combination would be very very low. LOL

6. I have one answer from a frequentist perspective and another from a Bayesian perspective.

7. M says:

I got an instant answer. But it looked like I am missing something. Then I spend some minutes wondering what I am missing…

And I figured…

That my first answer is right.

1. Lazy T says:

I too think your 1st answer is right. I can’t see a catch unless it’s too dark to see.

8. Chris Emerson says:

After coming up with 2 answers which were immediately dismissed, got the right answer in about 45 secs. At least I think it’s right!

9. In the dream with talking dog I take a red pill from his bag

10. Koenfucius says:

I think there is not enough information: the likelihood that the original pebble is black (or white) is not known.

1. Edgar 2(there seem to be more than one of us!) says:

Absolutely. My conclusion too.

2. Chris Emerson says:

Is not not safe to just assume 50/50 then?

3. NoAstronomer says:

Agreed. Knowing the original probability is necessary. Like Chris I went with 50/50 and had the answer in seconds.

Mike.

11. Anders says:

Didn’t we just have this puzzle? It feels very familiar

By the way, who won the “best answer” competition for that balance sheet thing?

1. Holden Caulfield says:

Wasn’t that a poodle with two bags of black and white stones? What is it Richard and dogs with bags of stones though? if I were Freud I think my answer would be unprintable, just aswell I’m not!

12. Bob O'H says:

There’s an infinite number of correct answers (and we can’t even count them all). It depends on what baggage we came into the alley with.

1. Anders says:

I’d actually say the chances are zero, because if a dog starts talking to me in a dark alley, I’m running away as fast as I can 🙂

But the probabilistic answer is very countable

2. Berhard says:

I think i would do the same as Anders… I even would avoid a dark ally with a nasty dog… even if he is not talking…

13. Andrew Westlund says:

Same as the others. Instead of thinking immediately of the odds of drawing the pebble as if it were done under normal circumstances, I can’t stop thinking of the dog…i settled on an answer after about 5 minutes of quizzically staring into space at my desk at work.

14. The fact that the dog talks is a distraction, to stop you remembering that dogs are colour-blind – and we only have its assurance that the there might be a white pebble in the bag, and not a light yellow one, for example… 🙂

1. Of course dogs are only red/green colour blind, so he can tell the black and white from each other, and others. Again, though, if the dog is talking to me, nasty or no, I’m going to be far too busy discussing his background and interest in maths puzzles to get round to trying to solve it. (ok, so I’m not sure where to start but I had you fooled, right?)

2. mittfh says:

Even if the dog is completely colour blind, it should be able to tell the difference between a white pebble (light) and a black pebble (dark). You know the second pebble is white (light), so I think you have to take it on trust that the dog isn’t lying when it claims the bag contains either a light pebble or a dark pebble.

15. Luis says:

The probability of taking a white pebble is 0%, as per Murphy’s Law.

1. Assuming you want a white ball – the question only asks your chances of getting one!

16. Baz says:

Years of experimentation by standup comics has established that you just don’t see white pebbles from a dog any more.

17. Berber Anna says:

Why is the dog nasty? As far as I can tell, all it wants to do is teach me probability.

The dog wants to teach you probability, therefore it is nasty.
Nice dogs want to play ball with you.

2. Berhard says:

I prefer probability teaching dogs.. it does usually not involve touchting salivaged balls…

19. vildmark says:

I pulled a Schrödinger cat out of the bag. What are the odds?

1. mittfh says:

Ooh, a lesson in quantum mechanics 🙂

The first pebble is in a a state of quantum superposition – it is both black AND white. However, of course, looking in the bag seals its fate so it can be revealed to be either black XOR white.

-oOo-

Seriously, if the probability of the first pebble being white was 0.5, then I have a solution. If it wasn’t, I haven’t.

20. and is it correct to assume the chance of the pebble that is allready in the bag is 50% to be black and 50% to be white ? otherwise you can never calculate this

1. I wondered the same, but I think we have to assume that, otherwise surely Richard would have said.

21. ChivNick says:

You did this same puzzle not so long ago only it was the devil, not a dog.

1. Nick says:

That was a different puzzle with a different answer. The Devil first drew a marble at random, found it to be white, and then asked the odds that the remaining marble was white.

22. About a minute. And another minute to confirm on paper. (And if it’s dark how can you tell.) Probably right.

23. Navneeth says:

I can say with 100% certainity that the answer lies somewhere in the interval [0,1).

24. Paul Durrant says:

The answer (ignoring the setting) seems obvious, so just a few seconds to solve.

Whether I’m right or not is another matter….

25. Savant says:

Was this a pre-arranged meeting? And what do you get out of it?

A pebble!

And you can’t even be sure what colour it is.

26. Sue says:

🙂 it is easy ~ took a second or two.

27. Anonymous says:

The only puzzle hear is why a nasty ally dog wants to play a whimsical game rather than maul the participant, is it the Golem of the canine world?
P.S had an answer within 5 seconds, and an explanation for that answer in under 5 minutes.

28. Katryn says:

I get famous for owning the world’s only talking dog. Who cares about a pebble?

i got the answer very fast, but I’m thinking there is something I overlooked, because this was just to easy…

30. Pedro says:

And if you take out a white pebble, what is the probability of you having left a white pebble?

1. NoAstronomer says:

Ooh, that’s a good one!

31. LucyUK says:

I think this took be about 10 mins to work out… I got confused to begin with and dismissed a few answers.

I soon can to another conclusion and worked that probability formulae which gave be a better answer.

Hope its right… looking forward to monday … and reminded me of my GSCE maths….lol

Lucy UK x

32. Jason F. Cannon says:

incredibly simple…. I hope. : )

33. Mickey D says:

2secs but explaining it took 20 secs.
Puzzle looked familliar haven’t we had a dog and pebbles before?

34. Greg23 says:

I think this one was all about trying to get clever comments.

35. John Loony says:

The answer is obvious, and the reason for the answer is equally obvious. Is there something I’ve misunderstood?

36. After the “holy ship a talking dog” I think I got it..and dog slobber from picking up the white stone. Yuch!

37. Jean-francois marchand says:

If the dog is nasty, would the original white pebble still be white?! Joke aside, seems like a it’s too simple to be so!

38. erikthebassist says:

Reminds me of a joke… So these two horses are in their stables talking to each other, and one says “I had a dream last night about running in the Kentucky Derby. It was amazing, I was running faster than I ever had in my life, and I won!”

The other horse said “yeah I’ve had that dream many times, in fact, I pretty much always dream about running.”

As the conversation winds on, a greyhound dog comes walking up and over hears them talking about dreaming about running and decides to join in “I’ve dreamt about running in a race many times, the thrill of chasing that rabbit is exhilarating!”

Both horses look at the dog for several moments before one finally says “ummm, yeah, right ok.”

Feeling like he’s being given the cold shoulder, the dog turns and leaves, head down, tail between his legs.

The horses just stand there for a good minute before one of them finally says “Holy crap, a talking dog”

39. Hey, it’s a nasty dog. There’s no way he’s going to let your hand anywhere near him without biting you! You are going to get stitches, not pebbles. 🙂

40. magicalan1-extramail@yahoo.com says:

Richard…..we talking a “change bag” here? After all, it was a nasty dog!

41. Good fun as always. I agree that the problem is insufficiently specified. Took me about a minute, making a reasonable assumption about the missing bit of information. (Would have been quicker, but I don’t practice on probability exercises often enough.)

I look forward to seeing the answer on Monday.

42. Jerry says:

Saw how to solve it immediately. Got a pen and paper to draw a picture of the problem and perform the calculations. About one minute.

43. Anonymous says:

No need to calculate anything. Assuming even odds that the first pebble is black or white, the answer is so obvious I had it before I finished reading the question. The real question is, what is the dog betting us?

44. Zach says:

10 seconds

45. Don’t tell me I’ve finally gotten the hang of these things. I figured it out in short order (unless I’m wrong), but it does seem easy. And I don’t think the darkness of the alley nor the nastiness of the dog can very much alter the color of the pebbles.

46. Marion says:

Got an answer quite quickly and am happy with it- just a little worried about the amount of alcohol I must have consumed to find myself in this position in the first place!!

47. Camel says:

Still trying to think what the catch is. There must be one….

48. Anonymous says:

Tell you what….unless Richard decides to post a rebuttal of the many, many “75%ers”, it won’t help the sales of his puzzle book.

Let’s see….if 50% of his solutions were correct, but he pulls out one incorrect solution for a promo, what is the probability that I will actually shell out money? 75% or 66%?

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