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.

Ok back to your hubby being on the show.
In the pub they are betting on total wins in the shows.
You say he will win 10. Back it with £1000.
No one else says he will win 10.
He does win 10.
Everyone else who bet 9,8,7,6,5,4,3,2,1 wins has lost.
The only person the landlord pays out is you.

What? If i was in the pub and i bet on 5 wins, i would get paid out, but i wouldn't get as much as you, because my odds would have been different to yours at the beginning, when we placed the bets before any games were played.

You say he will win 10. Back it with £1000

It's very hard to get 10 wins in a row.
So the odds I would want are:

2/3 ^ 10 which is definitely not 1 / 1024.

The chances are I will lose. But there is only 1 way to help that bet win and that's by swapping every time. From the start. And always swapping.

No your betting on total wins.
Total being the final number.

The landlord only counts the result of a show.

Yes the swap does not guarantee a win.
Yes you swap to give yourself a better chance.
But the chance only related to the doors as you open them.
Once you have opened the door that factor of the puzzle is done, finished, ended. No longer relevant.
Your landlord only cares do you have a car.

The landlord only counts the result of a show

I have absolutely no idea what you are talking about.

Ok, so we're back to forecasting the W/L chances , much like with the coin flip guessing where you bet HHHHHHHHHH will happen and i bet HHHHHHHLLL. The odds will be the same at the start, but if the coin lands heads first 10 times running, you win. The coin is slightly different though because the odds on each flip are 50/50, whereas the doors are weighted 33/66

Why are we in a pub now? And are we playing with doors, balls, cards or Rugby teams?

Your landlord only cares do you have a car

And that is why you need to do a large 'pub' study.

Yes - you can tell the landlord yes I have a car or no I don't have a car.
But that's just an answer to a question.

"If he asked 99 people the same question - assuming all of them had been on the show and none of them had swapped, how many people do you think would have won a car?"

If you can answer that question correctly, then you have understood.

I've confused my loses and my tails, for L read T

nd are we playing with doors, balls, cards or Rugby teams

Come on Italy ....

I thought the pub was an easy way to show that car, no car is a 1/2 thing.
No one in the pub cares about door odds.
They just want how many shows in a row were won.

They just want how many shows in a row were won.
Why would they want this info though?

Why does the pub need 99 men ?
They only care about Mr Chomalungma their mate.

I thought the pub was an easy way to show that car, no car is a 1/2 thing

But it's not.

Because you need to have a lot of people so you can get an idea of the number of people who win and the number of people who lose.

Someone just saying they 'won' or 'lost' gives no idea of the probability.

If you have more people saying whether they won or lost, then you cna get an idea of the best strategy.

You need large numbers.

There's a law for it.

en.wikipedia.org/wiki/Law_of_large_numbers

I'm tying myself in knots here trying to work out what you're asking. So in the pub they're betting on 10 wins in a row? If it were coins then the odds would be 1/1024. But at the point the doors are presented as 2 doors to the contestant, they are weighted. Therefore the betting odds would be different at the start.

They only care about Mr Chomalungma their mate

The smart money would be on a win if they swapped.
The people who don't understand probability wouldn't know.
The smart money would be on a loss if they didn't swap.

(Assuming they want to know if my hubby (who doesn't exist) just won a single game)

I am not really worried about 10 games in a row,
That's irrelevant.

BTW - do you agree that it is ALWAYS better to swap, no matter?

I'm not joining in the pointless argument with mummy..... however to the person offering 6/1 on Italy winning the 6 nations.... can I bet on this please?

With the proviso I get 6/1 on all the countries. As I will then bet £1000000 on them all. And win £7m for my £6m stake :-).

Pedantry is what I do.

So at work on Monday, how did you spend your weekend?
I spent it debating maths on the internet

Work would probably get that about me

Doors inc. don't need more shows it only has a 10 show run.
We are agreed on the probability of contestants winning the game increases by swapping the door.
The pub is ONLY interested in betting on MR C. They don't care about Joe Blogs.
All the landlord wants is can MR C win 10 times. This is a one of bet. So the odds are only related to MR C.
Can he win a car each week or not.

There are two outcomes, but those outcomes are not equal probabilities.

You are roughly 1000 times more likely to get 10 in a row if you go for the host's door. It's still unlikely (about 1.7% chance), but statistically much more likely than if you pick the original door.

We are agreed on the probability of contestants winning the game increases by swapping the door

YES!!!! From the start.

Thanks

I have closure

Can he win a car each week or not
The odds of 10 wins in a row are 2/3 ^ 10 assuming he swaps at the start.

That is NOT 1 in 1024.

The landlord doesn't care about your odds being weighted.
The game is recorded as a win or a loss.

Question on a test paper.
Odds of winning a game show ten times in a row....
Answer. 1/1024.

If the landlord is offering bets on the assumption that a competition with two possible outcomes has a 50% chance of being won then he's thick as mince and soon to be bankrupt. Does he offer the same on Nadal, since he can only win or lose?