Take your age .....
- Thread starter Sharky
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Drago
Legendary Member
- Location
- The Urban Fringe
what witchcraft is this?!
Dogtrousers
Lefty tighty. Get it righty.
Dogtrousers
Lefty tighty. Get it righty.
Here's a fun one I saw yesterday.
Your friend has chosen one card at random from a standard pack of cards. You have to guess what it is. Before you guess you can ask one of two questions which your friend will answer truthfully.. The questions are:
A. Is your card red or black?
B. Is your card the ace of spades?
Which question gives you a better chance of guessing the card?
Your friend has chosen one card at random from a standard pack of cards. You have to guess what it is. Before you guess you can ask one of two questions which your friend will answer truthfully.. The questions are:
A. Is your card red or black?
B. Is your card the ace of spades?
Which question gives you a better chance of guessing the card?
They are both the same.
A cuts the deck in half, giving you a 1/26 chance
B effectively gives you two guesses (ace of spades and one other), which doubles your chances giving 1/26
A cuts the deck in half, giving you a 1/26 chance
B effectively gives you two guesses (ace of spades and one other), which doubles your chances giving 1/26
ColinJ
Puzzle game procrastinator!
- Location
- Todmorden - Yorks/Lancs border
I reckon that is wrong!
I think that the odds in case B are 1/52 (card is an ace and you guess the right suit) + 1/48 (card is not an ace and you guess the right suit) so option B is better?
It's completely black and stumbling through the sock drawer, containing ten black socks and ten brown socks.
What is the minimum number of socks do I need to grab, to ensure I have a pair.
What is the minimum number of socks do I need to grab, to ensure I have a pair.
3
The first two could be different, but the third will match one of them
The first two could be different, but the third will match one of them
Dogtrousers
Lefty tighty. Get it righty.
I think you might have misunderstood. It's either A or B. Not both. In A you ask the colour, not the suit. In B you guess the ace of spades (or any card really) not the suit. You never guess the suit in either case.I reckon that is wrong!
I think that the odds in case B are 1/52 (card is an ace and you guess the right suit) + 1/48 (card is not an ace and you guess the right suit) so option B is better?
The simple explanation is that in case A you get one guess at a half sized pack, and in case B you get two guesses at a full sized pack. Both the same.
But if you want to look at it more closely ...
In case A if they say yes it's red, you now have 26 cards (the red ones) to choose from. So your chances are 1/26. Same if they say no it's not red and you choose a black card. So chances in case A are 1/26.
Case B is a bit more complicated.
If they say yes it is the AoS you will definitely guess right because now you know what the card is. There's a 1/52 chance of that happening.
But if it's not the AoS you get a second go. There's a 51/52 chance of this happening and this time your chances of guessing right are 1/51. So we add these together:
(1/52) + (51/52 * 1/51)
= 1/52 + 1/52
= 1/26 same as case A
There's a bit of misdirection in the question because case B specifies a particular card (AoS) If it had just said you get to guess twice it would feel more plausible.
If you still think it just feels wrong (as I did) feel free to write a simulation in excel (as I did
) and you'll find that it's right.
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ColinJ
Puzzle game procrastinator!
- Location
- Todmorden - Yorks/Lancs border
Sorry, multitasking so distracted - I read it as "Is the card an ace?"!I think you might have misunderstood. It's either A or B. Not both. In A you ask the colour, not the suit. In B you guess the ace of spades (or any card really) not the suit. You never guess the suit in either case.
The simple explanation is that in case A you get one guess at a half sized pack, and in case B you get two guesses at a full sized pack. Both the same.
But if you want to look at it more closely ...
In case A if they say yes it's red, you now have 26 cards (the red ones) to choose from. So your chances are 1/26. Same if they say no it's not red and you choose a black card. So chances in case A are 1/26.
Case B is a bit more complicated.
If they say yes it is the AoS you will definitely guess right because now you know what the card is. There's a 1/52 chance of that happening.
But if it's not the AoS you get a second go. There's a 51/52 chance of this happening and this time your chances of guessing right are 1/51. So we add these together:
(1/52) + (51/52 * 1/51)
= 1/52 + 1/52
= 1/26 same as case A
There's a bit of misdirection in the question because case B specifies a particular card (AoS) If it had just said you get to guess twice it would feel more plausible.
If you still think it just feels wrong (as I did) feel free to write a simulation in excel (as I did
