Poll: A little math problem

[Jumplion]

I believe the correct answer is "Fuck Math".

In Russia, math fucks you!

Actually this sort of math is extremely important in business, even more so in science. Failing to understand such basic statistical functions can lead to poor investments or failed designs. Suppose an available investment is a company with two copper mines, both of which must strike copper to make a profit. From the scientific analysis of similar mines, each mine has a 50% chance of striking a workable copper vein. One of the mines already has struck copper. What's the chance the other will also strike copper? If the investment is $1,000,000 but the possible profit is $2,750,000, is it a mathematically sound investment or not? If you know the chance of a fuel rod failing from a defect is 50% and one of your two fuel rods has failed, what are the odds your new death star is going to suffer complete power failure?

Math is much more likely to fuck you than the reverse.

The trick to the question is that it populates the set with things - namely, a pup and its sex - whose probability spread you intrinsically understand. If the set were sixty randomly selected molecules each with a 0.003% chance of being contaminated, you would probably see the problem as a set problem rather than as simply guessing the sex of a second pup.

Imitation Saccharin, the question was the probability of the second pup also being male, not the probability of either pup being male.

OH, OH, OH! Okay, now I understand, I remember seeing a problem or two like that (most notably in the movie "21"), now I get why it's 33%.

But the one thing that's nagging me is that, lets say, if the other copper mine struck, erm, copper than the other one still has 50% chance without putting the one that struck copper into effect....right? But unless that fuel rod was in direct explosive radius of the other fuel rod, the one that was defective still wouldn't have any real effect on the other one.....

Okay, maybe I don't get it yet.

And Seymor, it's just a math problem calm down, jeez. so get back to your probability homework young man!

 

[Captain Wes]

edit -- but idgaf i just found this login on a website so i could educate you fags.

and this kid is a 3rd year math major, so fuck you
AND THATS THE WAY IT IS

no, it isn't. I've listened to your arguments and responded, you just keep saying the same thing in the same way only with insults. Very intelligent

 

[LV Solace]

I'd assume a third year math major would have a descent grasp on grammar, and typing skills, not to mention common descency. CAPS locking, and using derogitory language is almost always a sign of immaturity, something that is not often found in third year math majors.

and your point is saying that the first beagle being male has a definite effect on the second beagle? It cant. a third year math major would know that.

 

[Captain Wes]

I'd assume a third year math major would have a descent grasp on grammar, and typing skills, not to mention common descency. CAPS locking, and using derogitory language is almost always a sign of immaturity, something that is not often found in third year math majors.

and your point is saying that the first beagle being male has a definite effect on the second beagle? It cant. a third year math major would know that.

thank you, i'm truly open to being swayed on this but just being a prick isn't the way to do it. Taxi driver almost had me on it but then I got caught up in the seymor and gained new vitality.

 

[LV Solace]

Actually independent events mean everything in this problem. And I'd like to think my avatar has nothing to do with my points, it's simply what I choose to represent my image.

 

[Jumplion]

God damnit!

I can't believe I'm being judged as a human being based on my grammar. It is not like that makes any difference. As long as I am understood, what difference does my usage of grammar make? Surely you have read Flowers for Algernon.

I can cut the ignorance with a knife. Its like they're trying to put words in my mouth. Independent events don't mean anything in this problem. I never said anything of the sort, LV Solace with the retarded anime avatar.

God, I hate internet forums.

Be that as it may, you're in the Escapist now.

A glorious place full of magic and wonder and cheap whores.

However, those cheap whores come at a heavier effort to obtain.

As such, they like politeness, correct punctuality, and being a good forum goer.

You however are name calling and making a math molehill into a mountain AND not to mention you're threatening us and being a general jackass.

Now be gone, and do your probability homework you have been telling us about!

And I like LV's avatar, it's so cute.

 

[imperialwar]

sorry but i gave up reading after the top of page 2.
The problem i have with the question is that the woman doesn't know the sex of the dogs, so when they get the dogs back from the bather unless he gives them an identifier, she still isn't going to know which one he had picked out to confirm the male.

 

[Jumplion]

I have to wonder though, can't they just check "down there"? Or, as GhostofSin said, it could be a hermphodite...

 

[milskidasith]

It's a badly worded problem, that's all. You could argue about it for days, but the point is, it wasn't clear enough to make you sure if it's 50% or 33%.

 

[Shivari]

If you know the chance of a fuel rod failing from a defect is 50% and one of your two fuel rods has failed, what are the odds your new death star is going to suffer complete power failure?

25% right?

The reason this problem tricked me is because of the wording. It's not testing my abilities, it's testing if it can trick me or not.

God damnit!

I can't believe I'm being judged as a human being based on my grammar. It is not like that makes any difference. As long as I am understood, what difference does my usage of grammar make?

I have no idea what some of your abbreviations meant, and the reason people are reporting you is because you're swearing like a sailor and generally trying to start a conflict.

 

[milskidasith]

If you know the chance of a fuel rod failing from a defect is 50% and one of your two fuel rods has failed, what are the odds your new death star is going to suffer complete power failure?

25% right?

It's a 25% chance they both fail... If one already failed, it is 33%, assuming they were both tested to see if they would fail at the same time. If you actually made one, had it fail, and made another with the same 50% chance of failing, it would be 50% because it isn't a set, just two seperate coinflips.

 

[Karka]

I admit I haven't read all the replies but here goes. The first dog has no bearing on the second dog, basic math explains that to us. Now, on to the second dog. The dog can either be male or female giving it a 50/50 chance. It's like a coin or anything that has two options. I have a minor in math this question just seems silly....

 

[Shivari]

If you know the chance of a fuel rod failing from a defect is 50% and one of your two fuel rods has failed, what are the odds your new death star is going to suffer complete power failure?

25% right?

It's a 25% chance they both fail... If one already failed, it is 33%, assuming they were both tested to see if they would fail at the same time. If you actually made one, had it fail, and made another with the same 50% chance of failing, it would be 50% because it isn't a set, just two seperate coinflips.

See, it just seems like a stupid misplacement of words that isn't really important. I don't see how it makes a difference if you flip two coins across the room and look at one, or if you flip one and then flip another. The second is independent from the first, it's still 50%

It's a stupid rule.

 

[Jumplion]

If you know the chance of a fuel rod failing from a defect is 50% and one of your two fuel rods has failed, what are the odds your new death star is going to suffer complete power failure?

25% right?

It's a 25% chance they both fail... If one already failed, it is 33%, assuming they were both tested to see if they would fail at the same time. If you actually made one, had it fail, and made another with the same 50% chance of failing, it would be 50% because it isn't a set, just two seperate coinflips.

BUT, if we count the two coins as a set then it would be 33% right?

It's like Shivari's saying, it's the damn wording of the problem. If the wording was correct, I might understand this a bit more, but it's a stupid trick question.

Hate trick-questions unless I'm the one telling them!

 

[werepossum]

SNIP
OH, OH, OH! Okay, now I understand, I remember seeing a problem or two like that (most notably in the movie "21"), now I get why it's 33%.

But the one thing that's nagging me is that, lets say, if the other copper mine struck, erm, copper than the other one still has 50% chance without putting the one that struck copper into effect....right? But unless that fuel rod was in direct explosive radius of the other fuel rod, the one that was defective still wouldn't have any real effect on the other one.....

Okay, maybe I don't get it yet.
SNIP

Nah, you get it. My examples were probably not that good, but in both examples the same principal - that knowing the value of one member of a set affects the probability spread of the other members' values - was the same as in the original problem. I was attempting to show (crudely) how this can be important for people other than engineers or mathematicians. If you randomly selected two mine sites and one struck copper, the chance for the second is that you randomly selected two winners, NOT the chance that any one mine will strike copper. Similarly, if you randomly select two fuel rods and one fails, the probability of the other failing is the probability that you randomly selected two defective fuel rods, NOT the chance of any individual fuel rod being defective. This sort of thing can be very important in engineering, although hopefully a critical component with a 50% failure rate will have more than one back-up. In any case, the probability function in question is the composition of the set you selected, not the probability function of each member's possible values.

A more likely scenario would be a system with five widgets, each with a 5% defective rate. If at least three widgets must be in working order for proper operation and one widget is observed to fail, what is the chance two more widgets from the five randomly selected for the system will fail? Now imagine the system is a $300,000,000 satellite and a repair mission costs $25,000. Do you schedule a repair mission, or do you wait and hope more widgets don't fail? Variations of this kind of problem are reasonably common, and an incorrect understanding of probability and statistics can sink a company.

My point was that understanding set probability versus sequential probability is important for everyone, but it can be VERY important for some.

The same thing can be expanded to include coin tosses. If you toss two coins, you will have a distribution of possible results analogous to the pup gender question. The result of each coin toss is independent from the other. But the probability of the set of both coin tosses follows a rigid structure. Knowing one coin's result changes the probability of the other coin's result. As Dirtface said, it's the Monte Hall problem.

 

[werepossum]

If you know the chance of a fuel rod failing from a defect is 50% and one of your two fuel rods has failed, what are the odds your new death star is going to suffer complete power failure?

25% right?

It's a 25% chance they both fail... If one already failed, it is 33%, assuming they were both tested to see if they would fail at the same time. If you actually made one, had it fail, and made another with the same 50% chance of failing, it would be 50% because it isn't a set, just two seperate coinflips.

Exactly correct.

 

[Shivari]

But the probability of the set of both coin tosses follows a rigid structure. Knowing one coin's result changes the probability of the other coin's result.

But it's independent from the other one. It's a stupid trick.

Or this might be way over my head and I should just leave. I take it you learn these evil and useless tricks in later years.

 

[Jumplion]

Great Wall of Text

Oh hO! Now I get it, yet again the wording of the problem is to blame.

And who is this amazing god-like being that discovered the root of this trickery?

Fine, I'll have your stick avatar running over people done by the end of the week, how's that sound?

 

[werepossum]

If you know the chance of a fuel rod failing from a defect is 50% and one of your two fuel rods has failed, what are the odds your new death star is going to suffer complete power failure?

25% right?

It's a 25% chance they both fail... If one already failed, it is 33%, assuming they were both tested to see if they would fail at the same time. If you actually made one, had it fail, and made another with the same 50% chance of failing, it would be 50% because it isn't a set, just two seperate coinflips.

See, it just seems like a stupid misplacement of words that isn't really important. I don't see how it makes a difference if you flip two coins across the room and look at one, or if you flip one and then flip another. The second is independent from the first, it's still 50%

It's a stupid rule.

It's not a misplacement of words. The only trick is that your mind leaps ahead to what you THINK you know.

In anything - science or math or engineering or English literature or love or cooking - there are things you know and things you don't know. Knowing what you know is even more important than knowing what you don't know because what you don't know MAY cause a wrong result, but not knowing (i.e. not recognizing) what you do know means you can't act upon that information, which practically guarantees a wrong result. Learning to recognize and correctly interpret what you know, or at least what you can know if you can recognize it, is absolutely vital for success in anything.

In any endeavor, learning to recognize and correctly incorporate what you know is the basis for sound work. Everyone here should make absolutely sure he or she understands this problem AND understands why natural human inclination is wrong in this case. How many times in life do you look back and slap your forehead, saying "How can I have been so stupid? It was all right in front of me. I knew he couldn't be trusted. I knew that answer was wrong. I knew that wasn't going to work."