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

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?

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

42

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.

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?

1 in 26 for all three options.

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.

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 ...

Once a card is pulled from the deck, the odds are out of 51, not 52...

Blast! Got the analysis right, blew the math....

I would ask, “What card do you have?”

---

Roswell, GA (Atlanta suburb)

I would ask, “What card do you have?”

POMTL!

---

I am that Masked Man.

All you can do, is all you can do.

There’s trouble — it's time to play the sound of my people.

Your boos mean nothing to me, I've seen what you cheer for.

Insisting on your rights without acknowledging your responsibilities isn’t freedom, it’s adolescence.

I've been to the edge of the map, and there be monsters.

We are a government of laws, not men.

Everybody counts or nobody counts.

When a good man is hurt,
all who would be called good
must suffer with him.

You and I have memories longer than the road that stretches out ahead.

There is no safety for honest men except
by believing all possible evil of evil men.

We don’t do focus groups. They just ensure that you don’t offend anyone, and produce bland inoffensive products. —Sir Jonathan Ive

An armed society is a polite society.
And hope is a lousy defense.

You make me pull, I'll put you down.

I *love* SIGs. It's Glocks I hate.

>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.

---

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.

"Show me the man and I’ll show you the crime."- Lavrentiy Beria

Don’t be a joker, what did the Guardian say?

---

Saint Cloud, Minnesota, where the weather is wonderful even when it isn't.

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

I found the answer.
[www.theguardian.com]

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

---

Roswell, GA (Atlanta suburb)