Mr. L's Probability 'Box' Quiz: (Answer revealed, DU gets a 100% on the quiz)

[mr_lebowski]

Last edited Thu Aug 8, 2019, 03:59 PM - Edit history (2)

There are three boxes, each with one drawer on each of two sides

++++++++++++++++++
+ drawer 1 +++ drawer 2 +
++++++++++++++++++

++++++++++++++++++
+ drawer 3 +++ drawer 4 +
++++++++++++++++++

++++++++++++++++++
+ drawer 5 +++ drawer 6 +
++++++++++++++++++

You are told each of the 6 drawers contains either a gold or silver coin, and that there are 3 of each coin in the drawers

A random drawer is opened, let's say it's drawer #3, and one of the coins is found.

You may now choose any of the other 5 drawers, and if the coin in the one you choose matches the original choice (i.e. both are gold or silver), you may keep both coins ... if not you get nothing.

Which drawer do you pick?

Let's let the poll run for a bit before explaining the answer

7 votes, 0 passes | Time left: Unlimited
	Drawer 1 or Drawer 2 or Drawer 5 or Drawer 6
	0 (0%)
	Drawer 4
	0 (0%)
	Doesn't matter which drawer I choose, odds are the same
	7 (100%)
	0 DU members did not wish to select any of the options provided.
Show usernames Disclaimer: This is an Internet poll

[rampartc]

1. chance of a match are 2/5 for each of the remaining drawers

[mr_lebowski]

3. It sure SEEMS that way, doesn't it?

Last edited Thu Aug 8, 2019, 11:37 PM - Edit history (1)

Edit: sry, I fckd up the question in the first place leaving an important part out

[mr_lebowski]

2. Kick for the AM Crowd

Kickety-Kick

[mr_lebowski]

4. As pointed out I fucked up the question and left a part out :)

SO THIS IS WRONG given the question:

EDIT HOWEVER, Drawer 4 is still the correct answer, explained in my reply below ...

The answer to question is: You choose drawer 4.

Here's why, in the simplest possible terms.

The configuration in the drawers will always be:
One box: (SS)
Another box: (SG)
Another box: (GG)

You can rearrange them however you want, but you WILL have these 3 combinations of coins in the three boxes.

...

[Shrek]

5. Where did you ever say the boxes would be SS - SG - GG?

The way it's worded I assumed equal likelihood of SG - SG - SG.

And if the distribution of the coins is random then the probability is 40%.

[mr_lebowski]

6. Oh, shit, I left that part out?

Last edited Thu Aug 8, 2019, 05:26 PM - Edit history (1)

Damn I'm an idiot.

You guys (sortof) got it right given the question as phrased.

[mr_lebowski]

7. Actually I believe I'm still correct on this, assuming boxes are filled randomly

I should've stipulated GS/GG/SS in the first place, but I believe I'm still correct about drawer 4 ... it's just not as big an advantage as 2/3.

I'll have the explanation as to why in a second.

[mr_lebowski]

9. PROPER EXPLANATION ... Still Drawer #4

Last edited Thu Aug 8, 2019, 11:27 PM - Edit history (6)

Edit: n/m, I'z wrong

Y'all are right, odds are same if put into the boxes randomly.

[mr_lebowski]

11. I corrected my answer at #9

Do you still think it's wrong?

[Shrek]

13. Give me a few minutes

I originally did a simulation over 1 million iterations using a random distribution, which is how I confirmed the 40%.

I'll tweak the code based on your narrative and see what happens.

[mr_lebowski]

14. While you're at it can you confirm my 'hat-coin-driven' simulation

That suggests better odds of Config 2 than Config 1?

As I said, I don't believe that ratio is critical to the 'answer', but it affects how MUCH of an advantage is gained by choosing the other drawer of same box.

I'm seeing on the order of 2/5 vs 3/5 but only on 35 iterations (14 vs 21).

THinking it may be 1/3 vs 2/3 though. Be REALLY weird if it's 50/50.

Did a few more ... I'm at 16 vs 28 atm ...

TIA

[Shrek]

15. It didn't seem to make any difference

You were correct about the combinations: SG - SG - SG shows up 40% of the time, while some combination of SS - GG - SG accounted for the other 60%.

But it didn't seem to affect the overall result. Drawer 3 and Drawer 4 matched up 40% of the time over 1 million iterations.

[mr_lebowski]

16. HA, my hat trick worked. Thanks for doing that :)

Last edited Thu Aug 8, 2019, 11:33 PM - Edit history (2)

Now, if I may, since you're standardizing to choosing 3 and hence comparing it to 4, can you also compare the likelihood of the following 'matches on' as well on for each iteration?

1 matches 3
2 matches 3
5 matches 3
6 matches 3

And let me know what each of those probabilities all are?

EDIT: Nevermind did simulations myself ... you're right, 40% for all of them.

The advantage conferred by the 2/3 rule in the (SG),(GG),(SS) configuration is offset exactly by the probability of the (SG)(SG)(SG) configuration. DERP.

Also ... if it IS (GG), (GS), (SS) always ... there's a 2/3 chance sticking with same drawer is better ... which was how I meant this problem to be

[Shrek]

17. Yep, I reached the same conclusion

Thanks for the diversion, it was a dull day.

[sdfernando]

8. Doesn't matter, odds are the same

forget all the fluff, this is what confuses and misdirects people. There are only 2 possibilities, either gold or silver, there for the odds for any drawer is 50/50.

Same as the old "sock" problem.

You have a drawer full of socks, 20 pairs total, 10 are while and 10 are black. The drawer is covered so you cannot see into it when it is opened, you reach in and pull out a pair, it is black, you do this 3 more times and each time you pull out a black pair of socks. What are the chances that on your 5th try you will pull out another pair of black socks?

Don't get caught up in the details so much.

[mr_lebowski]

10. Edit: n/m I'z wrong

Last edited Thu Aug 8, 2019, 11:26 PM - Edit history (1)

[Ptah]

12. Are you M.C. Escher?