Search results for:

Gabes. . . the obligatory 'if you spit' question:

If you split I would be interested in the frame.

Done it, on-line. painless (almost). Took 5 minutes.

Only question I had a problem with was 15- What is your ethnic group? As a mongrel with no clear group that I know I never normally answer this one. I wasn't allowed to proceed without writing something so ended up with
B. Mixed/Multiple ethnic groups/any other Mixed/Multiple ethnic background. (write in) -Mixed
Stupid question.

There is no box for 'racist' which I find a bit racist.

^yes, each specific sequence is equally likely but it depends on whether the order has to be considered.

The problem (as usually stated) is what are the chances of flipping a head 100 times in a row. Rather than in an arrangement of 100 coins what percentage of possible arrangements feature XXXXX (XXXX being whatever you are measuring).

As useless was pointing out, many individual sequences give the same number of heads and tails if that is all you are interested in.

So with 4 coin tosses the possible outcomes are:

HH --- 1/4
HT --- 1/4
TH --- 1/4
TT --- 1/4
Therefore a head and a tail (order not important) = 1/4 + 1/4 = 1/2

They are all equally likely but if the order is not important it is 2 times as likely to get a head and a tail.

Well, strictly speaking you are not twice as likely to get a head + tail (on a two coin toss) when accepting combinations in place of sequences, the results aren't influenced by the rules you are using, only your interpretation of the results, but I understand the point you are making.

If a run of 'x' coin tosses was repeated infinitely many times each possible sequence would occur

Probably, but not necessarily.

I once had a long ongoing argument with a whole studio (around 20 people) where I worked (this was when the lottery first started so probably around 1995) - based loosely around this problem, basically a guy on the radio had said, during a piece on the lottery, that it was a mistake to choose all even (or all odd numbers) as those combinations are much rarer than mixed even and odd sequences.

It literally took me a month to convince people that the idea was nonsense, so strong was people's instinct that certain numeric sequences are significant in a system like this, it actually got quite funny at times, hilariously so, the whole thing ended in me actually making 49 little balls with 'Carry On' stars replacing the numbers to try and break the connection (and significance on sequence) people can erroneously place on numbers.

I got them to argue the case that:

Hattie Jacques, Sid James, Jim Dale, Terry Scott, Windsor Davies . . . (etc etc)

. . . was more (or less) likely to come up than . . .

Kenneth Williams, Charles Hawtrey, Joan Sims, Barbara Windsor, Leslie Phillips . . . (etc etc)

. . . and to explain the system by where one Carry On film star was more likely to be chosen than another, did the system need to know who was on the ball for instance, if we pained over all the 'Carry On' stars faces with green paint, obscuring them, would Hattie Jacques be still more (or less) likely to be chosen than Kenneth Williams.

I eventually became victorious, proud in having brow beaten 20 heathens into logical submission, but all the time I was slightly saddened knowing that while I had spent the best part of a month playing with my balls the guy on the radio was probably going out, getting pissed, getting laid and enjoying himself.

[/weeps]

Yes but if heads came up 100 times in a row the chance of me noticing and shouting this from the rooftops 100% . .

: )

Yep, that's basically the problem with people misunderstanding lottery probabilities.

47, 17, 8, 12, 2, 36 looks insignificant.

Whereas . . .

1, 2, 3, 4, 5, 6 looks significant.

And this significance is ascribed a value it doesn't have (it being more or less likely that other sequences we ascribe no significance to).

Over 100 coin tosses, there are 2^100 possible distinct sequences, and they're all equally likely (ie, 1 in 2^100 chance of each).
However, some outcomes can be reached by more than one sequence, so they're more likely to occur.
For example, there is only one way to get either all 100 heads or all tails, so those outcomes are vanishingly unlikely (2^100 has something like 30 zeroes).

All the outcomes are vanishingly unlikely, a row of 100 heads no more or less that any other outcome.

Chances of heads 100 times in a row 1 in 1,267,650,600,228,229,000,000,000,000,000
Chances of any sequence in 100 flips 1 in 1,267,650,600,228,229,000,000,000,000,000

However, take the outcome 1 head and 99 tails ... there are 100 sequences that give you the outcome, so it's 100 times more likely to come up.
The outcome 50 heads and 50 tails can be accomplished so many ways, it's much more likely to occur: look up 100 choose 50.

But, each of these sequences is individual and as likely to come up as any other outcome. Think it as a 100 bit binary system where each coin is a row of 100 coins needs to be set to 0 or 1 (heads or tails).

100 bit binary = 1,267,650,600,228,229,000,000,000,000,000 variations (1.267 nonillion).

But surely in the case of only 100 tosses (fnarr) 100 heads in a row would mean a coin that'd been tampered with?

No need for coin tampering, in fact no need for coins at all, as a purely mental exercise you can see how a heads > heads > heads > heads > heads > heads > heads > (etc) outcome is as likely as any other.

Shouldn't it even itself out to 50/50 over the full 100?

No, there is nothing pushing the system to 'even itself out'.

Whereby 50 heads in a row is equally likely as 50 tails in a row, or heads-tails-heads-tails-heads-tails etc or any other combo as you say?

Yep, all combinations are equally likely.

xD

Yep, it's an idiot tax.

was it the ipod that when on random sometimes played the same song twice in a row, as should be expected if the songs are selected at random. The music selection software was changed after complaints to make it "more random"

It's 'pseudorandom' rather than 'random'.

I would guess, from what you wrote, that Apple made the selection less 'random' to get around this, they would have stuck a stage in the PRNG (pseudorandom number generator) that simply checked the output for a duplicate of the previous output and if found got it to try again.

Sharing the winnings with all the other clever clogs who picked 1-6 would be a bit annoying though? ;)

31 FTW apparently (avoids birth date pickers)

Yep, all that stuff should be taken into account, but that is 'outside' of the maths, once we know the maths we can factor in things like buying the ticket as late in the week as possible (as you have more chance of dying if you buy the ticket earlier).

What about those born on the 29th of Feb?

Those numbers assume a 365 day year.

I used to wonder about the probability of winning the lottery on a lucky dip ticket, as you were asking the same numbers to be randomly selected in a 14m:1 chance twice.

You mean once when they are selected in the shop and then once again when they are selected in the actual draw ?

I think you are getting some stuff wrong here, the odds of getting those initial random numbers have no bearing on the odds of those numbers being selected in the draw.

So it is still 1 in 14m - rather than 1 in 14m x 14m.

The fact that they know each other is as good as irrelevant. While I guess there could be some very slight biases (people might have some connection to a shared event). and also there may be certain dates which someone is more likely to be born on (for example if people have more sex in winter), but for this question lets assume neither of these has an effect. Let's also assume there are no leap years & leap seconds, Again, this is to simplify the mathematics.

That means that for two (or more) to share a birthday it's

1/365 + 2/365 + 3/365 + 4/365 = 10/365 = 2.7% chance.

People --- odds of a shared birthday
10 --- 11.7%
20 --- 41.1%
23 --- 50.7%
30 --- 70.6%
50 --- 97.0%
57 --- 99.0%
100 --- 99.99997%
200 --- 99.9999999999999999999999999998%
300 --- (100 − (6×10−80))%
350 --- (100 − (3×10−129))%
366 --- 100%

This is something my friend used to do while believing in some kind of esoteric processes, faith and destiny instead of mathematics.

He had 49 tiny pieces of paper with number from 1 to 49 written on them. Every Wednesday afternoon he'd put them into a cup, shake it it take out six or seven pieces of paper depending on the lottery. I think he actually worked against the rules of probability.

My mum once asked me to fill in her lottery card, to save time pissing around I just rattled off 1,2,3,4,5,6 - she told me I wasn't taking it seriously and that 1,2,3,4,5,6 would never come up, I tried to explain that it was as likely as any other sequence, regardless of how hard I tried she couldn't believe it.

I told her that those numbers are as likely to come up in that order and every week for the next year as any other out come.

She simply wouldn't have it, she doesn't let me do her lottery card anymore.

Does probability have memory?

No.

The system might have a memory of some kind, but probability doesn't.

Does the fact that the 20 sided dice roll easier than the 6 sided one have any bearing on anything?

No.

If you could make a 24 sided dice and put each of the numbers 1-6 on 4 sides would each number have the same chance of being rolled as on a 6 sided dice?

Yes.

Would the distribution of the numbers over the sides have any bearing on this, ie if all four ones were on adjoining faces and all four twos were on adjopining faces and so on would the probablility of rolling any number be different to if the numbers were distributed sch that no two adjoining faces had the same number on them?

No, distribution makes no difference.

But should you wonder what is the probability of calling it right twice in a row, both flips you have a 1 in 2 chance of getting the right answer, but getting both the first AND the second correct is 1 in 4. Because both flips are 1 in 2, multiplied together gives 1 in 4. This can carry on, making the probability of 100 heads in a row, not impossible, but highly improbable.

The probability of 100 heads in a row is identical to any other combination.

Soon the light will shine out of my ass! Success at last.

"Light, even from beneath, always lights above"

No that's the new high powered led torch I swallowed for a bet.

"The man who gambles wins only his past"

you forgot licking you balls CG.. lol

i saw this somewhere...

"Truth is the breath of my life"
"Humility is the key to success"
"Hate is the subtlest form of violence"
"A good man's thought never goes in vain"
"Happiness depends on what you
give, and not what you get"

Anyone can turn out that kind of trite word salad - just sling together a few truisms and overly simplistic moralizing platitudes and you too could be the next Deepak (or any of the thousands of demagogic gurus churning out this shit).

"Truth is the glowing light within us all"

"Humility is the key that unlocks the knowledge of the soul"

"Hate is the dark shadow of the heart"

"Shoes are like gloves, but for your feet"

etc etc . . blah blah blah.

I could probably write a very simply little piece of scripting that could churn this banal shit out for if you want, just think you only need hit a key and some random wisdom is generated to guide you through your day.

: P

I was tired and did not bother explain myself properly.

I was playing the part of someone who was religious. They were talking about someone else of another faith who was an extremest and did like them, "That crack pot guy from region XXX is barmy!". They also however were admitting that there were some people of their own faith, however because they, them-self believed in the basic ideals they had some sympathy for the extremist of their faith. It's was only the extent to which they took the idea. For an example I used the idea of killing gays. Two people believing in the same idea but taking it to two different lengths. One who thought you should kill gays the other saying, "no it's a metaphor, we just mean discourage gays, killing is taking it to far", but yet believing in the same illogical ideas, but believing because they are placing a limit on there actions their ideas are somehow more valid than the extremest from their faith who places no limits on their actions.

Still not explained very well, but I really need to do voices and stuff to explain things better. Ideally a puppet show using my old socks. I have a favourite sock for each religion. You should see my Scientology sock. It's very dull.

I understand now, basically people more readily excuse extremism in their own religion, but I would still like to see the puppet show using old socks.

See.

It's 'its', not 'it's', as I've said before, elsewhere

Its a curse put on me by the jews.

..itchy

I heard that if you cut one in half it turns into TWO gays. That's not natural, that. No wonder everybody's so worried.

That's true, as it says in the Bible the only way to kill a gay is to eat it's brains.

Zealot!

Zealophobe.