Settle an arguement

Sam Vimes · 12-01-2007 11:46AM

the answer is obviously 42, or in this case 1/42

i71jskz5xu42pb · 12-01-2007 11:59AM

Somewhat related probability problem that puts people in a spin

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Have a think and then check the answer

Lothaar · 12-01-2007 01:04PM

PaschalNee wrote:

Somewhat related probability problem that puts people in a spin

Have a think and then check the answer

This 'problem' is a red herring. We're working with incomplete information, as we don't know anything about the presenter. Based purely on the information we have, as you phrased the problem, there is no advantage or disadvantage to switching your choice.

Back to the OP, as I said earlier it is a matter of phrasing. And I think it is entirely possible that Tusky misrepresented his mate's stance because they are talking about different things - one is the probability of rolling a 6 on the *next* throw, the other is the probability of rolling a 6 multiple times in a row.

i71jskz5xu42pb · 12-01-2007 01:19PM

Lothaar wrote:

This 'problem' is a red herring. We're working with incomplete information, as we don't know anything about the presenter. Based purely on the information we have, as you phrased the problem, there is no advantage or disadvantage to switching your choice.

Why do you need to know anything about the presenter? Three doors, you pick one, one of the remaining two, containing a goat, is opened. Is it to your advantage to switch your choice?

There is an answer and and it is not that "there is no advantage or disadvantage to switching your choice". So try again.

Kipperhell · 12-01-2007 01:33PM

THe problem is the terms being used and phrase. Probability is the incorrect term to use when you say the probability of 5 is coming up on the last time is wrong . The chance or odds remain the same on each throw but the probability of the series of throws coming up the same is a different concept and uses a different formula as stated. So it is more the statement doesn't make sense as you can't the probability of one throw.
People often missuse the word in english and think "probability" is the same as chance. So the odds of 5 coming up are still 1/6 no matter how many roles but the probaility of 5 coming up again is dependent on the number of roles.
So the statement you made is incorrect by not making sense you can't get the probability of one event as such.

Lothaar · 12-01-2007 01:36PM

Did you read that wikipedia entry? It contains a detailled discussion on the various incarnations of this problem and the lack of information in some incarnations, such as the one you used.

"In general, without the behavior of the host completely specified, it is not true that switching will be successful two-thirds of the time."

Tusky · 12-01-2007 01:42PM

Lots of replies, cheers people!

Its all been cleared up now.

The original arguement was this :

If I roll a dice and get any number (lets say 6). I still have a 1/6 chance of rolling a 6 the second time. He disagreed with this and was arguing that there was less of a chance of rolling the same number again, which of course is wrong.

I can see where the confusion was though. In his head, he was thinking about the chances of rolling 2 or 3 sixs in a row...which of course if less.

It was more a problem of phrasing it wrong...although from the very start of the arguement I said "we are both right....we're just phrasing things wrong". H on the other hand was adamant that I was just completely 100% wrong.

kevmy · 12-01-2007 02:34PM

Capt'n Midnight wrote:

don't forget it doesn't matter which order they come out in

42/6 x 41/5 x 40/4 ... :1

You are of course correct an oversight on my behalf.

kevmy · 12-01-2007 02:39PM

seamus wrote:

The lotto is a great example of this. There is an equal chance of 1, 2, 3, 4, 5, 6 coming up in a draw as any other grouping of numbers. Yet if we all saw this come up, it would be national headlines, and we'd be saying "Wow! What are the chances?!". Instinctively, most people don't choose sequential numbers, or scoff when their quick pick give a sequence because they think it reduces their chances. I would admit to feeling "cheated" when my quick pick gives me a sequence of three or more numbers, even though it's not rational.

Like the time that the Lost numbers almost came up (4, 8, 15, 16, 23, 24[a reversal of 42]) everyone thought it was weird and it is but still has the same chance as any other set of numbers

Manic Moran · 13-01-2007 10:56PM

As my Backgammon book put it, the dice have no memory.

NTM

rediguana · 13-01-2007 11:09PM

I didn't read other posts, so apologies for repitition.

Indeed, any given roll of a dice is equally likely to turn up a five (or whatever), 1/6.

Perhaps your friend is confused as the likelihood of throwing TWO CONSECUTIVE fives is less than the probability of throwing a five in a GIVEN throw.

The chance of throwing (say) ten consecutive fives is very low but, on the eleventh throw, the chance of throwing a five is still 1/6.

What a world!

InFront · 13-01-2007 11:14PM

I think the answer could have been made clear in one post if the op had been clearer tbh!:p
42... no, 43 posts on this question:eek:

Settle an arguement

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