Can you can guess the month another person bought their Golf?

The answer is - they're all correct!

This is the "joy" of statistics and probabilities. Take Lotto as an example. If you play each week with the same numbers, the law of averages suggests that one day you'll win. The problem is that each time the draw is done, the probability of getting the correct numbers is the same each time.

So in the original example, yes you have a 1 in 12 chance of being correct at the first guess (assuming you cannot see the car and peek at the rego label) but once you are down to 2 choices, you have a 1 in 12 chance of still being correct and a 1 in 2 chance of choosing to correctly change or not change. The 11/12 is slightly dodgy but still correct - the dodgy part is that it's not actually the probability of the other remaining month being correct but rather that your original choice was incorrect. Of course if you know in advance that no matter what month you choose, 10 of the months will be removed from the list, then you have a 1 in 2 chance of being correct because you'd put less effort into the original choice.

The other problem with this is the mathematical assumption that the choice is totally random. By the choice not being random, as in this case as someone is attempting to make what they believe to be an educated guess, the odds are different again.

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Originally Posted by elephino

The answer is - they're all correct!

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Thanks for making it past all of the distractions (it is like an ADD test!). However, the answers are mutually exclusive so only one answer can be correct under the random scenario applying.

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Originally Posted by elephino

This is the "joy" of statistics and probabilities. Take Lotto as an example. If you play each week with the same numbers, the law of averages suggests that one day you'll win.

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If you live to be well over 1,000 years old the laws of probability might be in your favour.

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Originally Posted by elephino

So in the original example, yes you have a 1 in 12 chance of being correct at the first guess (assuming you cannot see the car and peek at the rego label) but once you are down to 2 choices, you have a 1 in 12 chance of still being correct and a 1 in 2 chance of choosing to correctly change or not change.

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If you understand the probabilities of each option and act accordingly, there is a 100% chance you will switch, and if you do so, a 91.67% chance you will win by doing so.

There is a poll on this forum showing 80% of people who responded would switch. But success on switching is determined by the underlying probabilities of 1/12 and 11/12.

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Originally Posted by elephino

The 11/12 is slightly dodgy but still correct - the dodgy part is that it's not actually the probability of the other remaining month being correct but rather that your original choice was incorrect.

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Your choice being incorrect is the same outcome as the other option being correct, so the 11/12 is not dodgy at all as it refers to the same outcome.

The other possibility is that your initial choice was correct and the other choice is incorrect, of which there is a 1/12 probability, not a 50% probability as Rocket36 has suggested.

So there is a 1/12 chance that switching will end in tears (not 50% per the view that because there are two options it is 50/50.).

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Originally Posted by elephino

Of course if you know in advance that no matter what month you choose, 10 of the months will be removed from the list, then you have a 1 in 2 chance of being correct because you'd put less effort into the original choice.

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All but two options are always eliminated.

No more or less effort is required in any event.

The probabilities are calculated on the basis that the game always involves only a random choice (guess) made with no extrinsic information or factors as a guide.

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Originally Posted by elephino

The other problem with this is the mathematical assumption that the choice is totally random. By the choice not being random, as in this case as someone is attempting to make what they believe to be an educated guess, the odds are different again.

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This scenario is intended to be totally random and analogous to the Monty Hall Dilemma discussed elsewhere in this forum.

OK, so maths was never my strong point but logic is.

It's simple, you have a 50/50 chance.

The two guesses are unrelated. All the first guess did was help pick one of the two options for the second guess. The odds related to being right on the first guess have nothing to do with the odds of the second guess.

If the guy had said from the start that you had to guess whether his car was built in May or August then you have a 50/50 chance of being right, right?

So how is the situation any different now??

You still have two choices, 1) stick with your first choice, or 2) pick the other option. That is a choice of two options to me, either of which could be right.

Adam

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Originally Posted by Rybky

OK, so maths was never my strong point but logic is.

It's simple, you have a 50/50 chance.

The two guesses are unrelated. All the first guess did was help pick one of the two options for the second guess. The odds related to being right on the first guess have nothing to do with the odds of the second guess.

If the guy had said from the start that you had to guess whether his car was built in May or August then you have a 50/50 chance of being right, right?

So how is the situation any different now??

You still have two choices, 1) stick with your first choice, or 2) pick the other option. That is a choice of two options to me, either of which could be right.

Adam

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You see, that's what I thought as well. But it turns out it's a lot more complicated than that for some reason. At the end of the day, isn't it still a 50/50 choice with a 50% chance of being incorrect?

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Originally Posted by maca

You see, that's what I thought as well. But it turns out it's a lot more complicated than that for some reason. At the end of the day, isn't it still a 50/50 choice with a 50% chance of being incorrect?

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I think everyone else is over thinking it.

Adam

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Originally Posted by maca

You see, that's what I thought as well. But it turns out it's a lot more complicated than that for some reason. At the end of the day, isn't it still a 50/50 choice with a 50% chance of being incorrect?

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yes. at the end of the day, that's all that matters. you can choose either may, or august- one in two, right?

ohhhh no wait. it's in the rules that even though you 1. can choose may, or 2. can choose august, it says in the rules that you have to count all the other months of the year in your odds, because you know that it WASNT built in january, feb, march, april, june, july, september, october, november, december.

so, we KNOW that it wasnt built in those months, right? apparently, when choosing either 1. may, or 2. august, the fact that you know that it wasnt built in all those other months, means that your chances are now 11/12.

they are now 11/12, when faced with a choice of either may, or august. 11/12. two choices, you get one pick.

one pick. two choices. 11/12. two to choose from, one chance. 11/12.

so. may or august. pick one. i would have thought that the chances of it being may, are 1/2. and the chance that it's august, is the other 1/2.

wrong. the chance that its may, is 11/12. AND, the chance that it's august, is 11/12. apparently.

and with that indisputable logic, i'm out of this debate. unless there's sheilas involved.

Since when were there rules??

Two choices. May or August. That is what you have to work with. Only one is right. So you have a 1 in 2 chance of picking the right one.

Sorry, everything you else you said is BS designed purely to invoke an argument.

Adam

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Originally Posted by Rybky

Since when were there rules??

Two choices. May or August. That is what you have to work with. Only one is right. So you have a 1 in 2 chance of picking the right one.

Sorry, everything you else you said is BS designed purely to invoke an argument.

Adam

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1. there are very clear rules in the ''monty hall dilemma'' thread, upon which this thread has a strong basis.

2. if you read that thread, you'll note that i am one of the biggest proponents for the 1/2 line of logic, which might also have been somewhat evident in my literary style in my post just above yours.

3. i wont respond/ provide feedback, but please feel free to outline just what, in my post, was ''provocatively argumentative".....

cheers,

scotty

Sorry scotty, didn't mean you specifically, I realise you were quoting other people there. I meant the "rules" and resulting theories are designed to provocate an argument. There wouldn't be any point posting it on a forum otherwise! ;-)

I am not going to read the other thread ... I have a life! :)

Adam

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Originally Posted by Rybky

I am not going to read the other thread ... I have a life! :)

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yes, well....... there were a few of us who proved that we dont, with the shenanigans in the monty hall thread, haha!

and no need to apologise- no matter what the debate/ argument [even heated], there's never any bad blood with me :) - it's all about Veedub love, after all!

cheers,

scotty