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Stupid prob/stats question

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09-26-2014 , 11:00 PM

I_lose

grinder

Join Date: Nov 2012 Posts: 506

Ok,
I just corrected my psych prof. (A PHD) some math. And now, I'm scared that I was wrong.... She said

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you'll need a deck of cards. Get a regular deck of cards and pull out all the face cards (jacks, queens, and kings) for each suit. You should have 12. Find an assistant to help you. Ask your assistant to test you. You should try to guess the SUIT ONLY for each card. Don't worry about whether it was a jack or queen or king. Just the suit -- clubs, spades, hearts, or diamonds. They should hold the cards so that you cannot see them. Then, you should guess what each card is. Have your assistant record whether or not you were correct.

Here is the tricky part. For one of the times that you do this, ask your assistant to show you the cards after each guess. They can lay them on the table as you go. The next time, ask your assistant to keep the cards from you even after you guess. In other words, this time, you don't get ANY feedback at all. For your report, address the following:

Compare your success rates to chance. Pure chance dictates that you should get 25% correct. How did your success compare to chance?

Did it make a difference if you got to see the cards after guessing? Why or why not?

For fun, you could try adding all the aces to the stack and do it all again. Now, your chance rate is at 20%. How well did you do?"

(We are discussing ESP)
I included this in my report

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(Maybe I shouldn’t point this out, but it was bothering me) Adding the aces back to the stack does not affect the probability of guessing correctly. With J, Q, K of each suit you have a 3/12 chance of guessing correctly (assuming no feedback). This is simplified to ¼ or 25%. Adding the aces brings the count to 4/16 (four spades, four clubs, four hearts, four diamonds), which again simplifies down to ¼ or 25%

There isn't something painfully obvious that I am missing is there? Cause I'm pretty scared I missed something and it's too late to pull back.

Thanks.

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09-27-2014 , 01:49 AM

VBAces

veteran

Join Date: Dec 2007 Posts: 2,502

First off, don't be worried about telling a professor something and being wrong. They'll at least know that you are thinking about things. In this case, though, I think she just had a brain fart. Certainly if you take all 4 suits of any rank and try to pick the suit you will have a 25% chance of being correct, adding a rank will not change that.

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09-27-2014 , 05:00 AM

MMSS

Pooh-Bah

Join Date: Jul 2013 Posts: 4,680

As far as I can tell you're right.

inb4 was a psychological test

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09-27-2014 , 05:46 AM

DiamondDog

Carpal \'Tunnel

Join Date: Jul 2007 Posts: 7,474

Prof's site and screen name?

Another thing that seems odd - if the assistant shows you the cards, that sure as heck affects your success rate doesn't it?

Say the first card is Q

and the second is J

that radically alters the chance of the next card being a

.

Or am I missing something? I'm assuming no replacement, but that must be wrong?

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09-27-2014 , 05:52 AM

MMSS

Pooh-Bah

Join Date: Jul 2013 Posts: 4,680

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Originally Posted by DiamondDog

Or am I missing something? I'm assuming no replacement, but that must be wrong?

One is a pure chance experiment, the other isn't. At least that's how I read it.

The one that isn't is when you aren't shown the cards. You just have to guess.

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09-27-2014 , 09:34 AM

NewOldGuy

Pooh-Bah

Join Date: Mar 2009 Posts: 5,935

A thinking player should get more than 25% correct on the second experiment, by counting removed cards. Your chance to get the final card right is 100%. The one before that at least 50% if not 100. Etc.

And adding the Aces back gives you an even greater advantage when shown each card after guessing, because you have more cards to count the removal of by the end.

But without seeing the cards you still have 25% on each suit not 20%, regardless of how many ranks we start with. That must be a mistake in the OP. Or you switched to guessing ranks after adding back the Aces.
EDIT: I see you pointed this out to the prof.

Last edited by NewOldGuy; 09-27-2014 at 10:03 AM.

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09-27-2014 , 10:19 AM

I_lose

grinder

Join Date: Nov 2012 Posts: 506

Yeah, with "feedback" your last several are going to be much more accurate, with the last one being 100%. I wanted to make sure that my point that the deck was still 25% each suit was right. (I knew it was but I started to doubt myself.)

Thanks guys.

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