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math puzzler from "The Guardian"
Posted by: Todd's keyboard
Date: June 16, 2021 01:34PM
A Facebook friend posted this puzzle from The Guardian.

A friend chooses a random a card from a standard deck of 52 cards and keeps this card concealed. You have to guess which of the 52 cards it is.
Before your guess, you can ask your friend one of the following three questions:

- is the card red?
- is the card a face card? (Jack, Queen or King)
- is the card the ace of spades?

Your friend will answer truthfully. What question would you ask that gives you the best chance of guessing the correct card?

Todd's Bales-Board
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Re: math puzzler from "The Guardian"
Posted by: Lux Interior
Date: June 16, 2021 02:11PM
Red? Eliminates 50% of the choices, regardless

Face?

- Yes ==> eliminates 40/52 - 77%
- No ==> eliminates 12/52 - 23%

Ace?

- Yes ==> Done!
- No ==> eliminates 1/52 - <2%

So, ask if it's face and hope for yes?
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Re: math puzzler from "The Guardian"
Posted by: anonymouse1
Date: June 16, 2021 02:55PM
Exactly the same for each of them:

For red, it's (26/52)/26
For face cards, it's (12/52)/12
For ace it's 1/52
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Re: math puzzler from "The Guardian"
Posted by: Will Collier
Date: June 16, 2021 03:02PM
42
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Re: math puzzler from "The Guardian"
Posted by: PeterB
Date: June 16, 2021 03:12PM
Quote
Lux Interior
Red? Eliminates 50% of the choices, regardless

Face?

- Yes ==> eliminates 40/52 - 77%
- No ==> eliminates 12/52 - 23%

Ace?

- Yes ==> Done!
- No ==> eliminates 1/52 - <2%

So, ask if it's face and hope for yes?

Right, but you haven't actually factored in the possibility of it being yes or no for each option. Figure this out using the sum and product rules of probability:

Red? (1/52) x (1/2)yes = 1/104, + (1/52) x (1/2)no = 1/104, 1/104 + 1/104 = 2/104 = 1/52 (1.92%)

Face? (1/52) x (12/52)yes = 12/2704, (1/52) x (40/52)no = 40/2704, 12/2704 + 40/2704 = 52/2704 (1.92%)

Ace? (1/52) x (1/52)yes = 1/2704, (1/52) x (51/52)no = 51/2704, 1/2704 + 51/2704 = 52/2704 (1.92%)

... therefore my answer would be that they're all the same probabiliities.

I think I did this correctly?

Edit: whoops, I see my arithmetic errors ... corrected accordingly. That's what happens when you type too quickly!




Freya says, 'Hello from NOLA, baby!' (Laissez bon temps rouler!)



Edited 5 time(s). Last edit at 06/16/2021 03:25PM by PeterB.
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Re: math puzzler from "The Guardian"
Posted by: anonymouse1
Date: June 16, 2021 03:15PM
Hmm, maybe so. Have to think about it.

Quote
PeterB
Quote
Lux Interior
Red? Eliminates 50% of the choices, regardless

Face?

- Yes ==> eliminates 40/52 - 77%
- No ==> eliminates 12/52 - 23%

Ace?

- Yes ==> Done!
- No ==> eliminates 1/52 - <2%

So, ask if it's face and hope for yes?

Right, but you haven't actually factored in the possibility of it being yes or no for each option. Figure this out using the sum and product rules of probability:

Red? (1/52) x (1/2)yes = 1/26, + (1/52) x (1/2)no = 1/26, 1/26 + 1/26 = 2/26 = 1/13 (7.69%)

Face? (1/52) x (12/52)yes = 12/2704 = 3/676, (1/52) x (40/52)no = 40/2704 = 10/676, 3/676 + 40/676 = 43/676 (6.36%)

Ace? (1/52) x (1/52)yes = 1/2704, (1/52) x (51/52)no = 51/2704, 1/2704 + 51/2704 = 52/2704 (1.92%)

... therefore my answer would be to ask if it's red, since this gives the highest probability of getting it right.

I think I did this correctly?
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Re: math puzzler from "The Guardian"
Posted by: btfc
Date: June 16, 2021 03:23PM
1 in 26 for all three options.
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Re: math puzzler from "The Guardian"
Posted by: anonymouse1
Date: June 16, 2021 03:52PM
Ok, here's my new analysis (numbers are rounded)

Red:
Yes or no makes no difference-either way, you end up having to pick 1 out of 26 cards, so the answer is 1/26, or 3.8%.

Face card:
You have 12/52 chance of a yes answer (23%). If the answer is yes, then you have a 1/12 chance of picking the right card (8%), so the answer for "yes" is 2%. If the answer is no, which occurs 40/52 times (77%), then you have a 1/40 chance of picking the right card (2.5%), so the answer for no is .5%. I'm not sure how to combine those; adding them is 2.5%

Ace
You have a 1/52 chance of yes, which is 2%. You have a 51/52 chance of no, which is 98%; you then have a 1/51 chance of picking the right card (2%), so the answer for no is 98%*2%, or 2%. So adding, the ace is 4%.

So picking the ace is the best choice, if I've got this right.
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Re: math puzzler from "The Guardian"
Posted by: btfc
Date: June 16, 2021 04:12PM
Red or black, 1 in 26 either way, so 2 in 52 combined odds, so 1 in 26


Ace of spades, 1 in 1 if correct, 1 in 51 if not, 2 in 52 combined, so 1 in 26.


Face cards, 1 in 12 if correct, 1 in 40 if not, combined is 2 in 52, so ...
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Re: math puzzler from "The Guardian"
Posted by: freeradical
Date: June 16, 2021 04:16PM
Once a card is pulled from the deck, the odds are out of 51, not 52...winking smiley
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Re: math puzzler from "The Guardian"
Posted by: anonymouse1
Date: June 16, 2021 04:37PM
Blast! Got the analysis right, blew the math....
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Re: math puzzler from "The Guardian"
Posted by: rgG
Date: June 16, 2021 05:27PM
I would ask, “What card do you have?”





Roswell, GA (Atlanta suburb)
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Re: math puzzler from "The Guardian"
Posted by: RAMd®d
Date: June 16, 2021 06:39PM
I would ask, “What card do you have?”

POMTL!





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Re: math puzzler from "The Guardian"
Posted by: mattkime
Date: June 16, 2021 07:02PM
>What question would you ask that gives you the best chance of guessing the correct card?

- is the card red?

50% chance either way, 3.8% chance of picking the card. (.5 * 0.038) x 2 = 0.038

- is the card a face card?
Yes - .231 * .083 = .019
No - .769 * .025 = .019


...im not going to do the last one and just say they're all equal.



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Re: math puzzler from "The Guardian"
Posted by: DP
Date: June 16, 2021 07:59PM
I would ask, “What card do you have?”

Yes! This!







Disclaimer: This post is checked for correct spelling, punctuation, and grammar. Any attempts at humor are solely the responsibility of the author and bear no claim that any and all readers will approve or appreciate said attempt at humor.
My name is DP, and I approve this message.
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Re: math puzzler from "The Guardian"
Posted by: Speedy
Date: June 17, 2021 05:25AM
Don’t be a joker, what did the Guardian say?



Saint Cloud, Minnesota, where the weather is wonderful even when it isn't.
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Re: math puzzler from "The Guardian"
Posted by: Lux Interior
Date: June 17, 2021 06:12AM
Quote
Speedy
Don’t be a joker, what did the Guardian say?

I'm a joker
I'm a smoker
I'm a midnight toker
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Re: math puzzler from "The Guardian"
Posted by: rgG
Date: June 17, 2021 06:38AM
I found the answer.
[www.theguardian.com]

I ought to get some sort of prize, just for that. smiling smiley





Roswell, GA (Atlanta suburb)
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