Take this quiz if you're smart

[wiegeabo]

The probability doesn't change depending on when we're asked what the probability is. It changes depending on when Tom (or the person choosing a door) makes his choice. Was the choice made before or after one of the options is revealed.

When you pick is the whole key to the problem. If all three doors are closed when you pick, you only have a 1/3 chance of getting it right. Even after a wrong door is opened, you still picked out of three and only have a 1/3 chance. That means, by subtraction alone, there's a 2/3 (1 - 1/3) chance the other door is right.

Had the wrong door been opened first, and then you picked, you would only have two doors to pick from, rather then three. And at that point it's a 50-50 option.


As for the problem, the second they were told one of the three of them would die, Tom had a 1/3 chance (he implicitly chose himself). When it turned out Dick would get to live, Tom still only had a 1/3 chance of dying, which means Harry must have had a 2/3 chance of dying.

 

[November Rain]

here is the question

Tom, Dick and Harry are in prison. One of them has been randomly selected to die in the morning, and the other two will be set free. Their guard knows which one will die, but none of the prisoners does. The guard is under strict instructions not to divulge the identity of the doomed man. Tom is desperate for any information beyond the fact that his odds of death are one in three. He begs the guard to throw him an informational bone. Finally, to shut him up, the guard agrees to reveal only the following: the name of one of Tom's fellow prisoners who will be set free rather than killed. The guard then says that Dick will be set free. After receiving this information from the guard, what is the most accurate calculation Tom can make of the probability that he is the doomed man?

Tom clearly makes his decision after receiving this information

 

[wiegeabo]

No, all Tom did after receiving the information was calculate the probability. Which is the same thing we're doing. And the probability was set before the information was given (it was set when one of the three men were chosen). Once they were told one of them was going to die, they all had a 1/3 chance.

In the game show analogy, Tom's not deciding which door to pick after he's told Dick will live (shown what's behind door number 1). He's deciding whether he should change his pick (switch his choice from door number 3 to door number 2).

 

[ck51100]

I got all five right....the second time I took it and had seen the correct answers. I didn't do so hot the first time.

 

[November Rain]

so this is what you're trying to tell me...

Tom's probability were really between himself and a collective known as 'other'

other contained 2 people so the probability it was between any peson would be 1/3

so the probability it was tom is 1/3 and the probability it was other is 2/3.

Also the number of people reducing other doesn't change 'other's' its overall probability.

the problem with this is looking at it from an inside point of view and an outside point of view...

because quite clearly from the other man's point of view, he would also stand a 1/3 of chance of survival from his pov while tom would now have a 2/3 probability in being killed.

it also makes a difference whether the random selection was done before or after the knowledge that one of them was or was not to be killed because tom's perception of having a 1/3 chance may have not been accurate from the get go.This quite clearly changes things.

I'll accept their answer and the logic, but personally i don't think its a practical approach.

it's like the two finalists in pop idol instead of having a 1/2 chance of winning actually have a 1/5000000000 from the entire population/people that applied for the contest. and they both think the other has a 4999999999999/500000000000 chance of becoming the winner

 

[wiegeabo]

so this is what you're trying to tell me...

Tom's probability were really between himself and a collective known as 'other'

other contained 2 people so the probability it was between any peson would be 1/3

so the probability it was tom is 1/3 and the probability it was other is 2/3.

Also the number of people reducing other doesn't change 'other's' its overall probability.

Exactly.

the problem with this is looking at it from an inside point of view and an outside point of view...

because quite clearly from the other man's point of view, he would also stand a 1/3 of chance of survival from his pov while tom would now have a 2/3 probability in being killed.

Again, that's right. (That's why this is the problem my old professor used to show us how bad our math intuition is.) From Harry's point of view (assuming he was also told), Dick is going to live, so there is a 1/3 chance he'll die, and a 2/3 chance Tom will die. All at the same time that Tom sees he has a 1/3 chance and Harry has a 2/3. And that's where human intuition has the problem. But probability is all about your point of view and when things happen in relation to other events.

it also makes a difference whether the random selection was done before or after the knowledge that one of them was or was not to be killed because tom's perception of having a 1/3 chance may have not been accurate from the get go.This quite clearly changes things.

True. If the guards had decided Dick would live before making their choice, Tom's survival is 50-50 because there were only two options to choose from. But because the guards didn't know Dick would live until after they made their choice, they each have a 1/3 chance because there were three options to choose from. And eliminating an option after the fact doesn't change that.

I'll accept their answer and the logic, but personally i don't think its a practical approach.

it's like the two finalists in pop idol instead of having a 1/2 chance of winning actually have a 1/5000000000 from the entire population/people that applied for the contest. and they both think the other has a 4999999999999/500000000000 chance of becoming the winner

That's a different situation. If you tried to pick the idol winner before any eliminations (assuming equal quality of performance), then it would be 1/5000000000 or whatever.

But after each round of eliminations, the audience gets to repick from the leftovers. So the next time it becomes 1/50000. And then 1/12. And eventually 1/2 (or whatever the numbers are). If the audience never got to change their vote before the first round of eliminations, then the chance any particular vote was right would remain 1/5000000000 throughout the competition.


If you want physical proof, you can try this experiment yourself. Get three playing cards; Ace, King, Queen. Put them upside down, mix them up, and always try to pick the Ace. Now, since any card is just as good as another when they're upside down, just always pick the one on the left as yours. Go ahead and flip up the one on the right side. It's either an Ace, or not (2/3 chance it won't be). No matter what comes up, though, it doesn't change what the left card (your card) will be. So go ahead and flip your card up. If you keep track, your card (the left card) will be an Ace 1/3 of the time, even though you eliminate one of the other options before turning up your card.

Now, change it around a bit. Flip up the right-side card. If it's the Ace, redo it. If it's not the Ace, throw it out, mix up the two remaining cards and repick one as yours. Now there will be a 50-50 chance of getting it right because you're basically rerunning the experiment with only two options. If you keep track this time (mix, flip right-side, mix again, then choose), you'll hit the Ace half the time.

 

[X-Chick]

Okay for that one, I see it as how Tom is calculating his own probabity. If he knows that one of the other two is being set free and not himself, then his odds of being the one to die are now 50/50, right? Its basically like having 2 apples and one banana. You have a 1/3 chance of getting the banana. If you remove an apple, you now have a 1/2 chance of getting the banana, right? How is this question any different?

 

[ShadowBoxing]

The sentences are only there to trip you up, not to give you proper information. I got 5/5.

 

[X-Chick]

I love how people keep posting their scores.

 

[wiegeabo]

Okay for that one, I see it as how Tom is calculating his own probabity. If he knows that one of the other two is being set free and not himself, then his odds of being the one to die are now 50/50, right? Its basically like having 2 apples and one banana. You have a 1/3 chance of getting the banana. If you remove an apple, you now have a 1/2 chance of getting the banana, right? How is this question any different?

The thing is, Tom doesn't get to make the choice, so Tom doesn't get new probabilities. Even after learning Dick is safe, Tom doesn't get to repick who is going to die. The guards have already done that, and that choice isn't going to change. So all Tom has to go by is that a prisoner was selected to die at random, and after the selection, it turns out Dick lives. There is still a 1/3 chance Tom dies, and 2/3 chance Harry dies. Before being told about Dick, they all had a 1/3 chance of death. All this new information does for Tom is give Harry the greater odds of dying.

In terms of the playing cards, Tom is like the left-side card, and Dick the right-side card. Even after you flip up the right-side card (Dick lives), the card you chose is still the same as it ever was (Tom). So there is still a 1/3 chance the left card is the ace (Tom dies) and a 2/3 chance the middle card is the Ace (Harry dies).

 

[X-Chick]

Okay, now explain number 2. Because I'm not trying to argue that I'm right and he's wrong, just that the logic he's using to prove how he's right makes no sense.

 

[wiegeabo]

I'm much better with math problems than grammar.

For number 2 (which I admit I got wrong because I didn't think the Buffalo one out thoroughly) is easier to figure out by process of elimination.

The "horse was a ringer" line sounds right when you say it out loud and put in the missing commas. It's grammatically correct, which is easier to see when he adds the extra punctuation.

His explanation for the Buffalo one is good, and its grammatically correct. (Buffalo buffalo buffalo buffalo = Bison from Buffalo confuse [other] bison)

The rat-cat-dog is grammatically correct, but like he says it's much easier to see with a tree diagram. Basically, the rat, being hunted by the cat, being chased by the dog, hides.


As for the correct answer; from what I can tell, the phrase 'raced past the barn' is being used as an adjective to describe the horse. You could rewrite the sentence as "The horse that raced passed the barn fell jumped" or as (slightly less accurately) "The racing horse that passed the barn fell jumped".

The problem is that the sentence ends with two verbs, and you can't tell how they apply to the noun. There are two verbs, but only one subject and object in the sentence for them to be applied to (horse and barn). But a grammatical sentence should be some form of subject-verb-object.

 

[ShadowBoxing]

I love how people keep posting their scores.

Well you're the one who told us to take the quiz

 

[Dan33977]

I answered questions #3 and #5 correctly and the fact that a lot of people didn't (73% and 84%, respectively) astounds me: they're basic, common brain teasers. His explanations for the correct answers of questions #2 and #4 are reasonable, but I still don't understand his reasoning for the correct answer of question #1.

 

[X-Chick]

I'm much better with math problems than grammar.

For number 2 (which I admit I got wrong because I didn't think the Buffalo one out thoroughly) is easier to figure out by process of elimination.

The "horse was a ringer" line sounds right when you say it out loud and put in the missing commas. It's grammatically correct, which is easier to see when he adds the extra punctuation.

His explanation for the Buffalo one is good, and its grammatically correct. (Buffalo buffalo buffalo buffalo = Bison from Buffalo confuse [other] bison)

The rat-cat-dog is grammatically correct, but like he says it's much easier to see with a tree diagram. Basically, the rat, being hunted by the cat, being chased by the dog, hides.


As for the correct answer; from what I can tell, the phrase 'raced past the barn' is being used as an adjective to describe the horse. You could rewrite the sentence as "The horse that raced passed the barn fell jumped" or as (slightly less accurately) "The racing horse that passed the barn fell jumped".

The problem is that the sentence ends with two verbs, and you can't tell how they apply to the noun. There are two verbs, but only one subject and object in the sentence for them to be applied to (horse and barn). But a grammatical sentence should be some form of subject-verb-object.

Actually, I told you the wrong one, 3 is the one I hate.

But yeah, for that one I didn't interpret what he wanted correctly so I picked the wrong one.

Well you're the one who told us to take the quiz

Seriously, not to see who is smarter than who, but to see if this guy's logic is faulty in his questions and if his explanations to his answers make any sense to you. There's one question in particular that I still can't understand how this guy thinks his answer is right.

Quiz

 

[Dan33977]

For number 2 (which I admit I got wrong because I didn't think the Buffalo one out thoroughly) is easier to figure out by process of elimination.

The "horse was a ringer" line sounds right when you say it out loud and put in the missing commas. It's grammatically correct, which is easier to see when he adds the extra punctuation.

His explanation for the Buffalo one is good, and its grammatically correct. (Buffalo buffalo buffalo buffalo = Bison from Buffalo confuse [other] bison)

The rat-cat-dog is grammatically correct, but like he says it's much easier to see with a tree diagram. Basically, the rat, being hunted by the cat, being chased by the dog, hides.


As for the correct answer; from what I can tell, the phrase 'raced past the barn' is being used as an adjective to describe the horse. You could rewrite the sentence as "The horse that raced passed the barn fell jumped" or as (slightly less accurately) "The racing horse that passed the barn fell jumped".

The problem is that the sentence ends with two verbs, and you can't tell how they apply to the noun. There are two verbs, but only one subject and object in the sentence for them to be applied to (horse and barn). But a grammatical sentence should be some form of subject-verb-object.

Exactly!

Actually, I told you the wrong one, 3 is the one I hate.

Seriously? Question #3 is a basic, common brain teaser. I still don't understand his explanation for the correct answer of question #1.

 

[Jerry!]

The sentences are only there to trip you up, not to give you proper information. I got 5/5.

 

[X-Chick]

Exactly!
Seriously? Question #3 is a basic, common brain teaser. I still don't understand his explanation for the correct answer of question #1.

3 a basic logic question which typically goes like this: A=B, B=C, so by the transitive property, A=C.

And yeah for 1, I don't follow his reasoning but after re-reading the question, I get it. I just read too fast the first time.

 

[November Rain]

I answered questions #3 and #5 correctly and the fact that a lot of people didn't (73% and 84%, respectively) astounds me: they're basic, common brain teasers. His explanations for the correct answers of questions #2 and #4 are reasonable, but I still don't understand his reasoning for the correct answer of question #1.

number one is a double negative...

the no and never contribute to always

like never not close the door=always close the door

unfortunately, the fact it's a common phrase in one way doesn;t mean it translates grammatically the same way to like someone who is learning english for the first time

 

[britrogue]

I am a very logical person. That guy sucks

 

[Outsiderzedge]

Again, that's right. (That's why this is the problem my old professor used to show us how bad our math intuition is.) From Harry's point of view (assuming he was also told), Dick is going to live, so there is a 1/3 chance he'll die, and a 2/3 chance Tom will die. All at the same time that Tom sees he has a 1/3 chance and Harry has a 2/3. And that's where human intuition has the problem. But probability is all about your point of view and when things happen in relation to other events.

I suppose if he was told both Tom and Dick were going to live, he'd still have a 1/3 chance that he'll die.

Relative probablity is, what we call in the real world, "stupid," as well as wrong. Probability is absolute and not relative to individual participants.

Harry has a 1/2 chance of dieing if told one of the other two men will live, meaning if we randomly selected a man to die a million times without it ever being Dick, then 500,000 times it will be Harry and the other 500,000 times it will be Tom.

 

[wiegeabo]

I suppose if he was told both Tom and Dick were going to live, he'd still have a 1/3 chance that he'll die.

Relative probablity is, what we call in the real world, "stupid," as well as wrong. Probability is absolute and not relative to individual participants.

Harry has a 1/2 chance of dieing if told one of the other two men will live, meaning if we randomly selected a man to die a million times without it ever being Dick, then 500,000 times it will be Harry and the other 500,000 times it will be Tom.

Actually, that intuition is wrong. Probability is is relative. It all depends on the point of view.

I flip a coin and look at it. Then ask you if it's heads or tails. You have a 50% chance of getting it right. Does that mean I have a 50% chance of getting it right? No. I have a 100% chance of getting right. By looking at it, I changed my probability (collapsed the probability wave if you want to go quantum mechanical with it). Yet no one else's probability of getting it right changed because I'm the only one who looked. Probability depends on the situation.

And looking at the problem, the guards never told Harry that Dick will live. So Harry still knows they all have a 1/3 chance of dying. And yet at the same time, Tom knows they don't (either it's 50-50 like you said, or it's 1/3-2/3 like I say, but it's no longer 1/3 for all of them from Tom's point of view).

And if you think Tom will die 500,000 times out of a million after being told Dick will live, try the experiment yourself. You will find that after Dick is eliminated from death, Tom only dies 1/3 of the time and Harry dies 2/3 of the time.

Again, it might be easiest to see with the cards. When you shuffle and put the Ace-King-Queen face down, there's only a 1/3 chance the left card is the Ace. Flipping another card up doesn't change what the left card is (the cards aren't reshuffled after one card is exposed). So the left card will still only have a 1/3 chance of being the Ace. Which means the other card has a 2/3 chance of being an Ace, even if its only because probability must equal 1 (100%) and 1-1/3 = 2/3.