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.

[Spamantha]

Roll a dice.

2, 3, 4, 5 or 6 and you win a penny
Roll a 1 and you lose a million pounds.

The odds are in your favour.

Is it a good bet to make?

[mummmy2017]

Many bookies when they get a big bet in go to other bookies and place the same bet to ensure they don't carry the bet.
In fact if the bookie offers better odds, on MR C winning the show 10 times the landlord could even win.

[chomalungma]

In fact if the bookie offers better odds, on MR C winning the show 10 times the landlord could even win

The bookies would offer the landlord the correct odds because they would ask him what the odds were of winning each game and then do the maths.

Have you heard of Betfair Exchange?

You can do 1 bet at Coral and then lay it at Betfair Exchange.

But you normally end up losing money - because the odds don't necessarily reverse themselves - and also there is commission.

But Betfair people know the odds.

[OffToTheMoon]

My question was with a 1/2 odds on a car win
The chance of 10 in a row is 1/1024

The only way this can be true is if the game show format changed and the contestant was only offered 2 doors at the start and they picked one at random.

But you don't like the game format to be changed to meet your maths, so you'll have to change your maths to meet the game show format.

[chomalungma]

Watching an interesting video on risk aversion?

There are 2 doctors who can do your surgery.

Dr 1 - they say "There is a 5% chance you will die in this operation"
Dr 2 - they have a 95% chance of surviving if you go with me?

Who do you go with?

[Spamantha]

Depends; if Dr 1s last 5 patients died, that means I'm safe.

Or so Consultant Mummmy2017 told me.

[waterlego]

But do the Drs know the probability of patients dying in their care? Because if not, then that means it’s just a 50/50 chance. The pub landlord said so.

[TabbyStar]

People tend to choose the doctor who states it positively even though the probability is the same.

[chomalungma]

This thread has been illuminating. Thanks for all the scenarios. Mummmy either gets it or she doesn't get it. Probably

[mummmy2017]

I get that this has happened.
My question was based on a coin toss logic.
The landlord gave two options at odds of 1/2.
For this question with a 1/2 probability for ten throws the answer is 1/1024.
This means hard for someone to win.

You could not accept this as you were too stuck on it being dependent on the odds of winning the car, which the landlord never was interested in.
Your question did not have a 1/2 probability.

It also showed me that people's need to be right means they refuse to accept that there are things that can be independent of each other.

[Lweji]

You could not accept this as you were too stuck on it being dependent on the odds of winning the car, which the landlord never was interested in.

But that is exactly why 1/2 may be wrong. He may not be interested, but that's crucial.

In fact, if players are equally likely to swap as not to swap, the odds of winning the car are 50%, but if players know statistics, and are more likely to swap, then the odds that the player won the car are higher than 50%.

[iseetodaywithanewsprintfray]

"It also showed me that people's need to be right means they refuse to accept that there are things that can be independent of each other."

Like a series of coin tosses?

[mummmy2017]

Because the landlord was expecting the game show to be the same as all games show, with a chance for the contestant to win or lose.
There for he has choose to use odds of 1/2.
Because his bet is based on his own choice of odds, his bet is right.

He can use this same 1/2 for any gameshow where someone wins or loses .
Say tenable. Did they win the money.
The Chase. Did the team win.

[mummmy2017]

A single coin toss is a one off event.
Yes independent of anything else.
But you can take the result of that and ask can it happened 10 times in a row.
So it becomes dependant.
But this has nothing to do with the coin toss of the friends to see who goes first.

[Lweji]

Because the landlord was expecting the game show to be the same as all games show, with a chance for the contestant to win or lose. There for he has choose to use odds of 1/2.

This takes us back to probability and possibility. There is a chance (possibility) that the player wins, but the associated probability is not 1/2.
In most games it's much lower, or it can be higher if the player is very good (or knows statistics).
The landlord can go on a 1/2 bet if he knows nothing about the player or the game, but it's in his interest to know more.

BTW, notice that there is no game where contestants are given a chance to win a car from only 3 doors where the show host shows them one of them.
When this situation arises, contestants have usually gone through several doors. Most times, the door with the car will already have been discarded, and in the end the players end up with three doors and a minor prize.

[Lweji]

But you can take the result of that and ask can it happened 10 times in a row. So it becomes dependant.

Oh, dear.
That is not the definition of dependant.

[chomalungma]

I am at work. Will this thread go into a new one. I am hoping so!!!!

[mummmy2017]

Oh did you win a car dear. Game 1 yes.
Oh did you win a car dear. Game 2 yes.
.......
Oh did you win a car dear. Game 10 yes.

Winning ten games in a row means the answer depends on each of the 9 shows before being won....
Or your chain of wins falls.

[mummmy2017]

Oh so used the a instead of the e.
Woops do.
Dependent.

[chomalungma]

I still want to know if Mummmy would swap at the start to double her chances of winning.

[lotsofoysters]

He can use this same 1/2 for any gameshow where someone wins or loses .
Say tenable. Did they win the money.
The Chase. Did the team win.

He can, but he'd be very wrong.

On average there's a 1 in 6 chance of a team winning on the Chase - that's how often teams win. To get 10 wins in a row in the Chase the probability would be 1/60466176 on average.
That's a lot harder than throwing 10 heads in a row.

If the gameshow was something like the Crystal Maze where most teams make it through to the end and win some amount of cash prize, the odds of winning ten times in a row are much more likely than 1/1024. So your landlord would lose out.

[OffToTheMoon]

My question was based on a coin toss logic.
The landlord gave two options at odds of 1/2.
If the original game was guessing heads or tails from a coin toss, then your question (and answer) is correct
* ... on it being dependent on the odds of winning the car, which the landlord never was interested in.*
But, the fact of whether a contestant won a car was NOT based on a coin toss, it was based on a weighted decision. The fact that the landlord was not interested, does not change the odds. Him 'not being interested ' would cause him to lose much money if he went ahead with his bets.

[OffToTheMoon]

I still want to know if Mummmy would swap at the start to double her chances of winning.
I'd be fairly confident betting that she wouldn't, not just for one game...

[chomalungma]

Please can someone start another thread and link to this one. I really need closure

[OffToTheMoon]

If Hussain Bolt was running a race against me, do you really think my chances of winning are 50/50? After all, i could win or lose?
So when you are telling your pub landlord there's a race between 2 people, and the result is one person (me) could either win or lose, do you think he'd be wise to bet on me winning 10 times in a row at 1/1024?