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Two of these rigs are packed slider-down, and one is slider up. Each rig is identical. You're standing on top of your favorite wingsuit object without any tools to re-close either of the rigs, so you've got to guess which rig is slider-up or you're in for a hurtin'.

So you choose one of the rigs (rig A) and start gearing up your wingsuit. While doing so, one of your buddies yanks open one of the two remaining rigs (let's say rig B), and finds it to be slider-down.

There are now only two rigs left, the rig you've chosen (rig A), and the untouched rig (rig C). One of these rigs is slider-up.

The question is: Statistically, are you better off staying with the rig you've chosen (rig A) or switching to the other remaining rig (rig C)? Or does it even matter at all?

Please enter your poll option before reading any replies

just stick your nose up the closed rig, if it smells like a goat, take the other one...

but i'm kind of curious on the result of the poll..
sorry for spoiling. ;-)

You really need to invest some money in pull-up cords.

You are statistically better off switching as on your first pick you had a p=0.33 chance while you now have a p=0.5 chance.

wtf?
might as well the story behind this one before Calvin or Karnowski chimes in... be the first to spin it!

or, did you get invited to be a contestant on "Deal, or No Deal?"

What Hausse said.

But I ran into a problem like this on an exam about ten years ago. As I recall, I got the question wrong. Something about picking from a set of doors on a game show.

Edit to add: I'm changing my answer now that I've had a chance to think about it. The correct answer depends on knowing whether your buddy (who opened one of the rigs) knew ahead of time which rig was packed slider up. If he did know which rig was packed slider up, and intentionally picked a rig packed slider down to open, then you're better off switching, because his action has no influence on the probability of your previous decision having been right. In this case, it was a given that, no matter which rig you picked, he would pick a slider-down rig to open before you jump. In that case, his action provides no new information, and your probability of having picked the right rig on the first go is still 0.33333. If you switch rigs, on the other hand, you now have a 0.5 chance of picking the right rig. So you should switch.

HOWEVER, if your buddy did not know which rig was packed slider up (and thus must have picked a rig to open at random), then he's just injected NEW information into the equation. If we assume that he selected a rig to open at random (and chose the slider down rig), then we now know that there are two packed rigs left. One is packed slider down, and one slider up. Your decision of whether to switch or not will have NO EFFECT WHATSOEVER on the probability of having a slammer opening or not. Statistically, in this case it doesn't matter if you switch or not.

Ah, that one's easy. Pick the one with 36 (or 34, 38, whatever you use for wingsuit). Doh!


(I just happened to read about Monty Hall problem not a long ago.)

Brilliant!

I dissagree. The initial choice and the second choice are independent. It is the elimination of one of the options that increases your odds from .33 to .50 for either of the rigs in the second choice.

1. Marilyn Vos Savant rocks!

2. Shoelaces work as a pull-up cord in a pinch.

Ghetto, It was SOOOOO hard for me not to post this first.


Ghetto is awesome. and I love your twist on the 3 door question.

When making a informed decision, and they all are, one must take into account all factors from the past and present, not simply re-thinking the immediate problem.

Who packed the rigs?

If your buddy randomly picks one and finds it to be slider down, I don't see how it has any bearing on your opening.

But if he knew ahead of time which one to pick, so as to intentionally avoid cracking open the slider up rig, then you might be better off switching.

But today I drove more than I slept so take this as you will

Exactly what I was going to say... unless he's wearing those kiddie velcro shoes of course.

Really, I don't think it matters at all whether or not the friend knows. I also think that your chance of being correct when switching is p=0.66, not just p=0.5. Now, let's cut the stupid technical math variables and use percentages like normal people

Let's also just ignore repeating decimals.

When you first choose a rig, you have a 33% chance of being correct. This means that you have a 66% chance of being incorrect. So there is a 66% chance that one of the remaining rigs is the slider-up rig.

If your friend walks over and pops open one of the other two containers and finds it to be slider down, it doesn't matter if he knew it ahead of time. If he doesn't, there's a chance that he would pick the slider-up rig on accident and ruin the puzzle, and your jump. That's why you can't just use this method as a way to give yourself a 66% chance of correctly making a 1-out-of-3 choice.

So. There is a 66% chance that the slider up rig is one of the rigs that you didn't pick, and we know that your friend opens one of these rigs and reveals it to be slider down.

The odds that you were wrong are still 66%. If you only have one remaining option, your odds of choosing the right rig if you switch is 66%, not 50% like somebody mentioned.

Besides, 33% + 50% != 100%.

Then again, I'm the one who was wrong to begin with and argued the foolishly incorrect perspective nearly to the death for several hours straight, so there remains a 33% chance that I'm wrong again

Let's just have Nathan flip a coin

OK here's the Wikipedia article that put the final nail in my coffin that fateful desert evening, if anyone's interested...

http://en.wikipedia.org/wiki/Monty_Hall_problem

why did you haul all three rigs up? you wouldn't have the problem is you just carried the one that was packed slider up in the first place. dang...that was easy and it would have been a much easier carry.

Jaymaster has a good point, We should have made you carry all of our rigs up that next jump because you were wrong. that's 2000' of backpain/anklepain free cruisin I missed out on.

PS- i really wish we had pics of those things we were writing in the sand, getting mad at each other on that long desert climb. those would be sooo classic. Joar's scribbles in the dirt.

The hike wouldn't have been the same without all your bitching and moaning

Funny.

I remember Dessert has 2 S's
cause which would you rather
have double? Sweet or Sand?

just have to keep you guys entertained. balance man. Nate's Epileptic optimism and motivation, and my realism.

Okay... Sorry for the long post. I remember learning(?) this way back in a class, so this weird problem is really eating away at me. After a nap, and spending way too much time on this, I have (likely erroneously) arrived at the following.

There's this thing called Bayes Theorem which basically tells us how to find probabilities of things, given that other related things have happened. The form I am looking at is the theorem combined with the law of total probability, which is weirdly retyped here as:
P(A given B) = [P(B given A) * P(A)] / [ P(B given A) * P(A) + P(B given NOT A) * P(NOT A) ]

Gah. It really looks prettier on the wiki page.

So, let's let
A = "your initial choice was a slider up rig"
B = "your friend opens a rig that is slider down"

We want to solve for P(A given B), or P(your initial choice was slider up, given that the rig your friend opened was slider down). Then we can subtract the result from 1 to see whether switching would have improved your chances. Seems logical enough, right?

So we try to assign numbers to whatever we can:

P(A) = P(your initial choice was slider up) = 0.33
P(NOT A) = P(your initial choice was slider DOWN) = 0.66
P(B given A) = P(friend picks slider down, given your guess is slider up) = 1
because only one rig is slider-up and if you picked it, your friend is only left with slider down.

(this is where I took a nap so bear with me)

The last term we need to find is P(B given NOT A), which is P(friend picks slider down given that your initial choice is also slider down).

Given that your initial choice happens to be slider down, your friend has two rigs to choose from, slider up and down. This is where the question of who packed the rigs comes into play.

Case 1: If the friend packed the rigs, he knows which one is slider up, so he will always be able to select the slider down rig from the remaining two, so in this case P(B given NOT A) = 1.

Case 2: However, if the friend did not pack, he must choose at random which container to open. Thus, he only has a 50/50 chance of picking the slider down, so P(B given NOT A) = 0.5 in this case. Yes, we know that the event B has already occurred, but this expression simply calls for its probability in the general case, before anything else happened.

Anyway, if you put all the above numbers into the expression and solve, you get that:
P(A given B) = 0.33 in the first case and 0.5 in the second case, so already there is a difference. Recall that A = "your initial choice was slider up" so if you switched to the other remaining rig, it would basically flip the outcome, so then P(slider up for you if you switch) = 1 - P(A given B) = 0.66 if your friend packed, and 0.5 if he didn't.

Phew.

I checked that a few times, yet something tells me that I've made a mistake somewhere, as Mr Ghetto's solution seems more intuitively correct.

Does anyone care to chime in with a correction? What am I missing?
Steve

you are missing the fact that you are dealing with Ghetto. And with that individual (who I would NEVER in my life put a mr in front of) you should always err on the side of being ghetto.

o.k., that sorta answers the suspected Calvin/Karnowski story...

now how would this apply to "Deal or No Deal?"

ONE- DO NOT group me with AK.
TWO- this is a story that a very embarrassed, but also very integral person admitted to being wrong in, I was the other side of the argument. (being RIGHT!) Why would you even think of grouping me with AK? he was not even there.


We love you AK. just we like we like the paper man targets at the shooting range.

Ahhh.... i feel bad. did I hurt its little feelings?


no really, AK is the man. you said yourself you love everyone bashing. because you know we are all just playing. RIGHT?


PS- AK/Wwarped as long as there is two or more boobs between us, me and AK can be grouped as much as you want. no boobs is ok also.

OK then, we agree that if the friend packed the rigs, the odds are as I described.

Now.. if the friend didn't pack the rigs, nobody knows which ones are slider up or down. There is a 33% chance that the rig you picked is slider up, and when he chooses one of the remaining rigs, there is also a 33% chance that he will open the slider up rig. If he ends up opening the slider down rig, he has effectively done the same as if he didn't know. You still have a 66% chance of being wrong initially, and hence benefiting from a change of mind.

The only difference made by him knowing or not knowing is that he has a 33% chance of popping the pins on the slider up rig, screwing up the whole game and fucking over your wingsuit jump.

Besides, what kind of friend would hide that information from you at the exit point if he already knew? That's something that I wouldn't do to my worst enemy, but maybe Karnowski.

Hey vid666, I still need to hear your tree story in detail..

haha, i cant believe this thing is still going on. Going back to the original problem about the host of the game show changing the door...the answer is just that hes an asshole and should have opened the door you wanted.

but thats just my stats 101 expertise talking.

btw, the vid (and I know its crappy) that I have from the turkey boogie is up on ghettos ftp and gravity pimps.

personal fav is movie 007, just saying

keep it real fellas

Agreed.

I was wrong, swithching does increase your odds. I first heard of this in the movie 21, and ignored it as a stupid movie quote, but from the wikipedia link I konw understand why your odds increase. I even did a diagram on paper to double check. Its just so damn confusing and goes against typical reasoning.

This woman rocks, I have read one
of her books, most of her columns,
she has the highest IQ, and has 1
of my favorite quotes regarding the
problem with education in America
which goes something like this:

For some reason in this country many
believe a knowledge of science & math is
nice but not necessary while knowledge
of sex being necessary but not nice.

Oh, and besides being wicked smart,
witty and cool/comfortable with sex,
she is also attractive, and married to
Robert Jarvik the guy who invented
the artificial heart.

http://en.wikipedia.org/wiki/Marilyn_vos_Savant