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.

So by not using the info your taking a 50/50 gamble of winning.

No.
Imagine you enter a sweepstake for the World Cup. 32 team names are placed into a hat. You pick a team at random. You get Iceland. You had a 1/32 chance of picking Iceland. Your friend picks Brazil. They had a 1/32 chance of picking Brazil. That does not mean that both Iceland and Brazil have a 1/32 chance of winning the World Cup.

Which is what you're saying about the doors. The door you stick with does not have a 1/2 chance of winning the prize, even if you had a 1/2 chance of picking it.

You get a chance to pick a team, from the 32.
Once you pick the team then you find out what odds your team hold.
Your odds of picking the winning team are still 1/32, because there are only 32 names to pick.

"Ok so the ODDS of picking the right door when faced with 2 doors is 1/2.
The probability is 2/3 due to prior knowledge."

Those correct odds are also due to prior knowledge. The odds of a 50/50 chance are... 50/50. (Or 1/1, evens)

The life left in this thread reminded me that even NASA managed to balls up probability calculations, with sadly tragic consequences for the crew of the Challenger space shuttle.

Maths and engineering nerds (which I have now outed myself as ...) might be interested ... (I learned about it as a massive Feynman fan )

en.wikipedia.org/wiki/Rogers_Commission_Report

Your odds of picking the winning team are still 1/32, because there are only 32 names to pick

Yes - because it's completely random.

It's the 6 Nations Rugby soon.

If I put all 6 names in a hat and people randomly picked on, I would have a 1 in 6 chance of picking the winner.

But if I was given the opportunity to look at the names of the teams, I think I could have a much better chance of picking a winner than if it was totally random.

I know which team I wouldn't be picking.

And once you know the odds and they are much more in Brazils favour - would you swap with your friend if she offered?
If it wasn't a random choice, would you have picked Iceland over Brazil if you knew Brazil were 5 times more likely to win than Iceland? Or would you say well, there are 32 teams so every team has a 1/32 chance and I feel lucky.

You're refusing to swap doors even though you know the odds are much more in your favour if you do.

I think the gambling industry makes a lot of money from people who find probability difficult and rely on luck.

Probabilities always work out in the long run.

The odds of the roulette wheel are interesting.

@mummy2017

There are two doors, one has £1,000,000 behind it, the other nothing. You get to pick one.

If you want, you can ask the game show host which door the money is behind. The host tells the truth to 99% of contestants and lies to the other 1% (selected at random).

Do you ask the host or just guess?

@spamantha

For one moment, I thought you were doing the 3 doors, guard lies or tells the truth routine

A variation on that routine

Wonder if OP still wants that poker game.

The odds of the roulette wheel are interesting.

UK (37 holes) or US (38 holes) ?

Never quite grasped why the US needed "00", I have to admit.

Of course if the host only lies to 1% you would take his word.
.
Gambling is a money making thing, and the favourite does not always win.
After all loads of people have won at 100 to 1 on the Grand National.

After all loads of people have won at 100 to 1 on the Grand National

But most lose. Which is why you have very rich bookies. It's a 100 / 1 for a reason.

Gambling is a money making thing, and the favourite does not always win

But in a game like the Monty Hall problem, roulette, BlackJack, Craps - the odds are what they are.

The casinos know the probabilities. They always win. The odds are in their favour. Play a game long enough and you will lose.

If you play Roulette, you get 35 / 1 odds
So if you win, you get £35 back plus your £1 stake.
But there are 37 numbers (or 38 if you play on some tables)

So the chances of getting the right number is 1 in 37.

You might be lucky and win after 5 goes.
But if you continue playing for long enough you will be down.

So basically, walk away if you win.

But gamblers think they are on a lucky streak. Or their luck will change.

@mummy2017

There are 6 teams in the upcoming 6 Nations rugby.

I am prepared to give you 6/1 odds on Italy winning.

Will you take me up on it?

If you don't want my offer, then try Coral.

They have Italy at 500 /1

In a 6 country championship.

Still, stranger things have happened. Look at Leicester.

But in games like the Monty Hall problem or Roulette, there is no skill.It's knowing the odds.

Kudos to those displaying immense patience!

But on the doors the contestants door still wins.
If the hosts door had won 10 times you would stick, because why?

This is great on the problem

Apparently lots of men came up with the answer and people were fine with it.

But when a woman explained it, lots of people said she was wrong.

What were the chances of that happening?

I found it much easier to understand when the number of doors was increased, for some reason.

If there were ten doors, when you pick your random door there is a 10% chance yours in the winner.

If 8 doors were eliminated completely at random, so the winning door may have been eliminated, then the remaining 2 doors would each still have a 10% chance of being correct.

But, in the MH Problem, the doors aren't eliminated at random - the winner remains.
So, if left with 2 doors (the one you chose and the one the host selected), your door still only has a 10% chance of being correct. Therefore, there is a 90% chance the other, remaining door is the winner.

It obviously makes sense to switch to the other door, even though there's still a 10% chance you'll lose.

If the hosts door had won 10 times you would stick, because why

The host's door will always win 2 /3 of the time.
The other door will always win 1/3 of the time.

It does not matter if the host won before. The odds of it winning haven't changed. The host's door will always be 2/3.

It's very similar to the original problem on here.

There's a thing called the Gambler's fallacy

More on the Gambler's fallacy

I found it much easier to understand when the number of doors was increased, for some reason

That's why I love the million door example.

I like this.

It's very much like on here

Buy saying you swap eberytime because the odds don't change your actually ignoring the possibility angle.
Because if the host keeps winning at some point he passes the 66 in a row mark and your changes of getting a winner by sticking becomes more likely.

Because if the host keeps winning at some point he passes the 66 in a row mark and your changes of getting a winner by sticking becomes more likely

No it doesn't.

The Gambler's Fallacy

The gambler's fallacy is the belief that the chances of something happening with a fixed probability become higher or lower as the process is repeated. People who commit the gambler's fallacy believe that past events affect the probability of something happening in the future.

This is a good one.

I throw a coin. The winner is the person who gets either 2 heads in a row or gets a heads followed by a tails in a row.

Who is more likely to win?