to ask if you can answer a question re probability (Maths question)

[Fainne]

So, say I have 20 cards in a pack.

I pick one. It's the Ace of Diamonds let's say for argument's sake.

I then pick another one out of the same pack of 20 cards the following day.

Am I correct in saying that the odds of me picking the same card is a multiple of the single odds?

So 1/20 x 1/20 = 1/400

?

Because I've someone telling me the odds are still 1/20 that I'll pull the same card.

What is the probability that OP has realised she's wrong and that's why she's no longer commenting and calling us all idiots?
I'd say 99.9%

While there is now more probably of their door having the prize, the game is now out of two door and that means I am now also being give a 50/50 chance of getting the right door

But each door has a different probability of being right.
That's the whole point.

So if you stick, the door you chose at the start still has a 1 in 3 chance of being the correct door.

The door will always have a 1 in 3 chance of being right. No matter how many times you play.

While there is now more probably of their door having the prize, the game is now out of two door and that means I am now also being give a 50/50 chance of getting the right door.

You have a 1/2 chance of getting the right door if you have no idea of what has happened and choose at random. You have a 2/3 chance of winning if you play the odds and pick the door that you know has more chance of having a prize behind it.

If somebody rolls a loaded die and somebody else guesses a number without knowing it's loaded, they have a 1/6 chance of picking the correct number even though one number is significantly more likely to be rolled. However, if they know it's a loaded die, they'd be silly to pick anything other than the biased number because they're statistically more likely to win if they pick that number.

@mummy2017 Give it up, you're wrong. You're in danger of looking as daft as the OP by continuing to argue black is white. @chomalungma has explained why you're wrong very clearly. If you can't see it, please just take my word for it.

@mummmy2017 - you don't have "a 16% more chance".
You originally had a 33% chance of winning, a 67% chance of losing. The opening of one of the losing doors gives you the option to stay with your 33%, or move to the 67%. So you should always move to the 67%, no matter how many times you play.

I can see that you have 2/3 chance their door has the price.

But if I face the new game as a new game I also have a 50/50 chance of opening the right door. When facing two doors.

If somebody rolls a loaded die and somebody else guesses a number without knowing it's loaded, they have a 1/6 chance of picking the correct number even though one number is significantly more likely to be rolled. However, if they know it's a loaded die, they'd be silly to pick anything other than the biased number because they're statistically more likely to win if they pick that number.

That’s not true. The whole point of a loaded die is a that it’s more likely to roll a particular number, it doesn’t matter whether the person guessing knows that or not.

But if I face the new game as a new game I also have a 50/50 chance of opening the right door. When facing two doors.

What do you mean by “face it as a new game” though? You can’t undo what has already happened (you’ve chosen a door, Monty has opened one of your non-chosen doors with no prize behind it) so you can’t change the probability.

As others have suggested, seriously go and try it with a friend or your partner! That’s what got it to click for my partner, you can really see it.

But if I face the new game as a new game I also have a 50/50 chance of opening the right door. When facing two doors

You have a 50% chance of picking one of the doors.
But you do not have a 50% chance of picking the right door.
Because the doors have a different chance of being right.
One of them has a 1/3 chance of being right. That's the one that you chose at the start.
The other has a 2/3 chance of being right. That's the one you didn't choose.

@mummy2017 The chances the second door rises each game.
2/3 first game.
4/6 second game
6/9 third game.

OMFG!! Geniunely jawdropping! I suppose if you keep going, the odds will rise to 66.6%

Carry on like this, and you'll be telling us that 5 out of 3 people don't understand fractions!!

That’s not true. The whole point of a loaded die is a that it’s more likely to roll a particular number, it doesn’t matter whether the person guessing knows that or not.

Well, yes. I didn't explain very clearly, sorry. If someone has a die that always lands on 6,for arguments sake, and someone tries to guess at random which side it will land on, they have a 1/6 chance of getting it right. That doesn't meant their choice has a 1/6 chance of winning. They're two different questions.

That's the same as the doors in monty Hall. Just because you have a 50/50 chance of guessing the correct door if you have a choice of two and pick at random, it doesn't mean the door you pick has a 50/50 chance of winning.

Ok - so you want to treat it as a new game?

So going back to the million card analogy.
You have picked a card.
I have removed all the other cards except one that I skipped and the one that you chose.

Now if someone else came along and was asked to pick a card - without knowing what had just happened - they would have a 50% chance of picking the right card.

If they knew that I had just removed 999,998 cards - and left the one that you picked and one other - and they knew that I knew where the card was - they should pick the card that I deliberately chose.

The difference in the 2 approaches is the knowledge the picker brings to the table.

Now if someone else came along and was asked to pick a card - without knowing what had just happened - they would have a 50% chance of picking the right card

Actually - I am not even sure of that...if there are 2 cards - and one of them has a much higher chance of being the one I want, if I randomly pick one of them, will I be right half the time?

Your new game is this.
The logical physical doors in front of you are 2 in number.
You are being asked do you want to open your door or my door.
Therefore you have a chance of a prize or a chance of a goat.
You win or you lose. That is 2 chances.
Forget the 3 doors they are in the past.
.

Actually - I am not even sure of that...if there are 2 cards - and one of them has a much higher chance of being the one I want, if I randomly pick one of them, will I be right half the time?

Yes, if you truly randomly pick. It's the same as putting two cards in a bag, one is the "winner", one is the "loser". If you pick without looking from the bag you have a 1/2 chance of picking the "winner" each time.

@mummmy2017 but that isn't your new game. Your new game is
Here are two doors. One has a 2/3 chance of having the prize behind it. The other obly has a 1/3 chance. Which one would you like to pick?

@chomalungma yep your right.
The knowledge is the key.
Also that physically you only have a pair of doors to open messy up the probability with the reality.

@chomalungma - yes, you would be right half the time. It's only more likely to the original player because they have more information (and, logically, should use that information). If the original player or indeed the game creator tossed a coin to guess the card, they would also be right 50% of the time, despite knowing (or nearly knowing) where the right card is.

*Well, yes. I didn't explain very clearly, sorry. If someone has a die that always lands on 6,for arguments sake, and someone tries to guess at random which side it will land on, they have a 1/6 chance of getting it right. That doesn't meant their choice has a 1/6 chance of winning. They're two different questions.

That's the same as the doors in monty Hall. Just because you have a 50/50 chance of guessing the correct door if you have a choice of two and pick at random, it doesn't mean the door you pick has a 50/50 chance of winning.*

Right, I’m with you. There’s a difference between “what are the chances I can correctly guess which number this dice will land on” and “what are the chances this dice will land on the number I have guessed”

The knowledge is the key.

As it is with most gambling problems.

Someone who knows nothing about tennis can randomly pick between two players in a match and they'd have a 50/50 chance of picking the winner if they picked names out of a hat. But someone who knows about tennis has a much greater chance of picking the winner if the match is between Roger Federer and Anna Kournikova. Neither of those scenarios changes the actual outcome, which is that Roger is much more likely to win.

@mummy2017 - if you actually can forget the three doors, so that you no longer knew which door was more likely, then yes, you have a 50% chance. But, assuming you do not have amnesia, given that you know which door is more likely, why wouldn't you pick it?

Right, I’m with you. There’s a difference between “what are the chances I can correctly guess which number this dice will land on” and “what are the chances this dice will land on the number I have guessed”

Much more eloquently explained. I'm better at stats than writing, clearly

Much more eloquently explained. I'm better at stats than writing, clearly

At least you can use the bold function, which I keep failing at!

If I am on the show then the chances with no knowledge is 50/50
With knowledge 33/66
Not really enough to sway me to swap from my door. I feel lucky.
If I have 99 goes then yes you swap, the more goes you have the more the probability kicks in and shows results.

Not really enough to sway me to swap from my door. I feel lucky

Felling lucky doesn't affect probability.