Bill Snedden

I've no doubt. I seem to regular discussing it a long time ago on usenet on one of the mensa NGs. IIRC, the debate ran for months and some people were still unconvinced.

Regards,

Bill Snedden

Clutch

Bill, Grizzly, you hit it on the head. I read this quote from beausoleil, and thought, "The classic example is Monty Hall -- now how badly would *that* screw up the probability sceptics here?"

Probabilistic reasoning doesn't come naturally -- at least, not to me. And this thread confirms what I've long thought: Virtually all of those critical thinking courses in all those universities and colleges are grossly deficient, since they don't teach basic probabilities.

It's awkward; when I teach it in my CT classes, there's inevitably a bunch of students who complain that they didn't sign on for a math class. I tell them, "You've obviously never taken a math class!"

beausoleil

Since I'm bored of arguing about dice, why don't we find out?

<a href="http://www.cut-the-knot.com/hall.shtml" target="_blank">http://www.cut-the-knot.com/hall.shtml</a>

Liquidrage

Gave it some more thought and I see where the 1 in 11 comes from.

It's really the same thing as saying, "how many possible outcomes involve a six". The fact that someone hands you the first six, doesn't change the total possibilities.

The Monty Hall scenario is totally different however.
It makes sense to change because it stands to reason that there is a different set of probabilities (50/50) as to which door with a goat would be revealed.

[ July 04, 2002: Message edited by: Liquidrage ]</p>

parkdalian

I can see the 1 in 11 probability is right when we consider "all the possible outcomes involving a six" but if someone hands you the first die and it is a six, I still say it is 1 in 6.

If you roll 2 single dice in a row and the first is a six, your chances increase to 1 in six that you roll 2 sixes. It's the same if you're handed one die first. Look at it another way, you're more likely to be handed a six first if both are sixes, in fact it's a certainty. All other combinations involving sixes (non double sixes) the die with the six have only a 50/50 chance of being picked first.

[ July 04, 2002: Message edited by: parkdalian ]</p>

Liquidrage

There's two views here.

If you roll two dice, and someone hands you one and says "ok now whats the other?".
In this case it's a one in 11 chance if someone just picked a die that is a 6. The person that handed you the die was under no condtion to hand you a certain one of the two dies.

Now, if you roll two dice, a red and a blue, and only when the red die is a 6 you need to guess what the chance is of the blue die, then you'd get your 1/6 chance of the blue die being a 6.

Synaesthesia

Ok, This dice problem sent me for a real run around the block. Seanie, I wholly sympathize!

That we are told that one of the dice is 6 seems to have the exceedingly stubborn tendancy to fix one of the die in my mind. I take it away and hold it in my hand, as it were and a somewhat amorphous die sits before me. The inference that the answer is 1/6th is very difficult to escape given this conceptualization. Cognitive illusions are so much fun.

I think I understand it now, but I'm not sure I wouldn't make the same mistake in another context.

Anyway, to the points of this post:

1)I would really be interesting in being infuriated at this Monty Hall problem. Anyone want to describe it or link to a description?

2)One of my summer projets is to teach myself as much statistics as possible. Could anyone direct me to the better internet resources on the topic. (Currently I have a rather substantial library fine...)

[ July 04, 2002: Message edited by: Synaesthesia ]</p>

beausoleil

1)I would really be interesting in being infuriated at this Monty Hall problem. Anyone want to describe it or link to a description?

seanie

Please, please , please, please can someone help me.

I can't get this problem out of my head.

As I said I've never studied any probabilities but I can see this should be a relatively simple problem.

But I can't get my head round it.

I still can't see what's wrong with my reasoning. Where is the miss-step I've taken?

I assume it's when I reduce the 11 possibilities to 6.

seanie

Just to clarify.

Beausoleil said...

Now I assume this is correct since everyone but me thinks the answer is 1 in 11.

But I can't see why it's correct.

When I proceed to discard 5 options without knowing for certain the identity of the dice that's a 6 why is that erroneous? Why can't I do that?

Does whatever error I'm making have a particular name like 'Gambler's Fallacy' does for other intuitive errors?

And if someone can explain it to me please don't refer me to 'Monty Hall'. I had a look at the link and I really, really don't want to go there again just yet.

My brain hurts enough already.