a little logical/probability/math problem for you (1 Viewer)

[andrew markworthy]

That wasn't what I meant. It's an expression of the probability of something happening, and isn't a certainty. Thus, if something has a 1/1 chance it means there is a probability that it will happen once in the number of trials in question, not a guarantee.

I accept that the maths part may be faulty - as I said, probability theory isn't a specialist area of mine (as you'll have gathered).

Incidentally, I played the (real) MP3 player on a 4 hour round trip today and no way is the track selection random - we got a lot of the tracks in the 40-50 numbering, then a bunch in the 0-20 range, then some more in the 80-100 range. As it turns out, this is an unexpectedly neat feature, as I'd put down the tracks in thematic groups, so we had a bunch of seventies new wave, then the Pet Shop Boys, etc, etc.

 

[Jeff Gatie]

This does not necessarily mean the random generator is not random. It is extremely difficult for the human mind to analyze random numbers because the mind seeks "patterns" where there are none. I work in the field of random numbers and a truly random pattern never really looks like one. In order to certify a random number generator, the iterations tested are usually in the hundreds of thousands to millions and not only are patterns seen in certain pockets of data, they are required for a generator to be truly random. Only after analyzing the total number of iterations does the randomness arise.

 

[Dave Morton]

This seems to have the hypergeometric distribution or the negative binomial distribution (if you're looking at time to first occurrance).

 

[george kaplan]

Not to be too pendantic, but you're talking about # of trials til first occurance, not time. Time would require considering the lengths of the events, and you'd be looking at complex random walks, such as continuous time Markov chains.

 

[andrew markworthy]

I know - I'm a professor of psychology. One of the ways in which you can easily identify 'random' numbers generated by a human is the complete absence or abnormally low frequency of consecutive or repeating numbers. However, we really are talking about lengthy sequences (e.g. 10 in a row drawn from a set of 20 consecutive numbers), which in a disc of 140 tracks is I think rather non-random. Of course it could just be a pure chance. It's the first time I've played the player for more than about half an hour and had chance to observe lenghty sequences. I shall endeavour to go on more long journeys.

 

[Jeff Cooper]

Of course you also have the problem that if the random play happens to play your favorite song, then you still don't know where on the list that song falls

 

[ScottHH]

Andrew,



1/1 = 100%, if something has a 100% chance of happening, that IS a guarantee. If something has a greater than 1/2 (i.e. 501/1000) then it is "probably" going to happen. If something has a 999/1000 chance it most probably is going to happen, but it isn't a guarantee.

When I listed the sequence of events, I was listing every possible outcome. We can then add the probabilities of each outcome in which we get the desired result. I made the math easier by stopping the trial when we got our desired result.

If you toss a coin twice, there are 4 possible outcomes, each with a 1/4 or 25% chance of occuring:

HH =1/4
TT =1/4
HT =1/4
TH =1/4

You are concerned with getting heads at least once. The chance of getting heads at least once is the sum of the probabilities of all the scenarios except TT. So it is 3/4 or 75%. Not 100%.

I cheated and did this:
H = 1/2
TH = 1/2 * 1/2 = 1/4
1/2 + 1/4 = 3/4

If you flip a coin N number of times, you will have a 0.5^N chance of getting all tails (never hearing your song). Although once you get to 7 trials, the chance of all tails is less than 1%, it never actually gets to 0%.

As for your birthday problem, this link says it is 23 people. I took a year of statistics in college and some linear regression in grad school, but it's a bit rusty, and I just couldn't come up with the formula to the birthday problem myself without my head starting to hurt :b

 

[Chu Gai]

Where is Marilyn Vos Savant when we need her?

 

[george kaplan]

He might mean 1:1 odds.

Please. Keep her away.

When it comes to probability, while her answers are always "essentially" correct, there are often subtle ways in which her answers oversimplify the results, and are either vague, or simply incorrect. And we're not talking about some complex idea like Borel sets, but something that could be quite easily explained in her column, but would require a few well-written paragraphs to do so. But it would also force her to admit that she was wrong, or not fully correct, and that's something she is unwilling to do.

On a few occasions I've emailed her about those, but she has never even bothered to respond, much less modify her answers in print.

The bottom line is, that while she is very smart, she also knows how to market herself. I don't doubt for a moment that she gets lots of questions she can't answer, but since she only prints the ones she can answer, it looks like she's batting a thousand.

She makes her living from looking like she can answer any hard question that people send in to stump her, but it's simply not true. You'd never see her on Jeopardy, cause while she'd do very well and know lots of the answers, she'd never allow herself to be shown missing any.

Of course she does occasionally publish letters from those claiming she made a mistake, but only when they're wrong and she can look right again. No matter how smart she is, I have no respect for someone who can't admit she doesn't know it all. Einstein was a lot smarter than her, but he had no problem admitting he didn't know it all.

 

[Chu Gai]

Gee george, it was only a light hearted comment!

 

[george kaplan]

Sorry Chu, no reflection on you. Just something I've been needing to vent about for a while now.

 

[Chu Gai]

I understand George. On a non-related note, I'd once taken a graduate course, as an older adult so I'd long since lost my intimidation of professors, and had been marked wrong on a particular question by him. As the class went over the problems, eventually we came to mine and as the prof worked out the answer on the board, I raised my hand and informed him he was wrong and explained why mine was correct. He didn't take kindly to it and even after I took the book out and explained why his logic was wrong, he was adamant about my not having understood what the author of the book meant. Anyways, I got curious and even after replaying his lecture (I taped them), I still thought he was the one in error. Turned out the author of the book was teaching in a neighboring college so I called him and arranged for a brief visit. I brought the exam and he concurred with me. Then to my surprise, he said since my class was at night, he'd be happy to pay a visit. Lo and behold, the next class, there he was, the author of the book, sitting patiently in the back. As the prof entered the room, he asked if there were any further questions regarding the past exam. Again I raised my hand and pleaded my case. He said something to the effect, "Well, since I can't get it through Mr. Gai's head why he's wrong, perhaps one of his classmates will be so kind as to show him the error of his ways." A hand from the back rose, and a voice said, "Well, he's right. You're off by a factor of two." The professor said that he didn't know the student and would he care to identify himself. The man rose and said, "I'm the guy who wrote that book." He held the book up and the class could see by his face and the picture on the back flap that it was the same person. Well, those two got into it for a few minutes and then the professor said, well I thought you meant this. Then the light went on in his head. He corrected my grade and I owed a debt of gratitude to a man who didn't have to do what he did.
So sometimes we're wrong, sometimes we're right, and sometimes the people who think they're right are wrong.

 

[Haggai]

OMG, great story! Straight out of the movie line scene in Annie Hall, where Woody shows up the pompous guy by pulling out Marshall Macluhan right there in the cinema, and then he says, "If only life were like this."

 

[andrew markworthy]

Um, I thought I'd clarified that point a few posts earlier?

 

[andrew markworthy]

Chu Gai, quite right. A professor who thinks he can't learn from his students is mistaken. However, there are far more occasions when it's the other way round.