OT maths problem

cacbyname · May 2007

When I was doing probability at school in Maths, I had an eccentric physics teacher at the same time who explained to us that all probabilities come down to a half - it can be a single coin toss, ten consecutive coin tosses, the odds of predicting the Grand National winner or of Elvis being found alive on the same day that aliens land in Trafalgar square. An event will either happen or it won't, hence the chance is always fifty:fifty.

For those who've had a sense of humour bypass operation, he advised us to stick to conventional theory that leads to answers like 1/1024 for exams and gambling.

andrewgturnbull · May 2007

<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by cacbyname

When I was doing probability at school in Maths, I had an eccentric physics teacher at the same time who explained to us that all probabilities come down to a half - it can be a single coin toss, ten consecutive coin tosses, the odds of predicting the Grand National winner or of Elvis being found alive on the same day that aliens land in Trafalgar square. An event will either happen or it won't, hence the chance is always fifty:fifty.

For those who've had a sense of humour bypass operation, he advised us to stick to conventional theory that leads to answers like 1/1024 for exams and gambling.
<hr height="1" noshade id="quote"></blockquote id="quote">

Wanna bet?

Phil Russell · May 2007

mmmmm... my wife is a maths teacher. She once asked a boy what he thought the chances were of winning the lottery. She said she could see the cogs whirring round as he thought about it. Finally he said '50 50'.
Surprised, my wife asked why he thought that was correct...
'Well', said the lad 'you either win or you lose'.

And for all you would be mathematicians out there ... show me how, in a sample of about 30 people, the odds of two of them having the same birthday (month and date, not year) is about 50 / 50.

Cheers, Phil

DaveyL · May 2007

I can answer the snooker one - the probability is zero. If it's a break, at least one ball has been potted, so the balls cannot all end up in their starting positions...

(I know that's not what you meant)

maddog_2cp · May 2007

I'll give the answer to the birthday one in a minute but you might want to try this one in the meantime:

Suppose you're on a game show, and you're given a choice of three doors.
Behind one door is a car; behind the other two, goats.
You pick a door - say, No.1 - and the host, who knows what's behind the doors, opens another door - say No.3 - which has a goat.
He then says to you, "Do you want to pick door No.2?" Is it to your advantage to switch your choice?

Drop bars are a historical accident...... discuss

DaveyL · May 2007

Yes! The probability it was behind door 1 was 1 in 3; the probability of it being behind either of the other two is 2 in 3.

maddog_2cp · May 2007

very good

Most people think it's 50:50 to switch, as the car is behind one of the two doors. So normally they say I'll stick with my first choice.

The answer to the birthday one is 23 people by the way.

Easiet way to undersytand it is if you start with one person in the room and add them one by one, and each time calculate the prob. that no match has been found

Prob(no match) with just 2 people is 364/365 (if we assume birthdays occur on all days of the year equally)

Prob(no match) with 3 people is 364/365 x 363/365 the third person must not match with either the first person or the second person

Prob(no match) with 4 is 364/365 x 363/365 x 362/365

and so on

the calc for 23 people is prob(no match) = 0.493

so for a room with 23 people there is a greater than 50% chance of a match

when it reaches 60 people it's 0.994

Drop bars are a historical accident...... discuss

maddog_2cp · May 2007

I should be working............

Drop bars are a historical accident...... discuss

DaveyL · May 2007

The birthday one is a good one. I believe the "choose one from three, then have one wrong choice revealed to you" problem also comes up in the book "The Curious Incident of the Dog in the Nighttime" where the mathematical proof is also given. I could be thinking of another problem though.

cacbyname · May 2007

<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by andrewgturnbull
Wanna bet?
<hr height="1" noshade id="quote"></blockquote id="quote">
As I said in the post: [:p]
<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by cacbyname
For those who've had a sense of humour bypass operation, he advised us to stick to conventional theory that leads to answers like 1/1024 for exams and gambling.
<hr height="1" noshade id="quote"></blockquote id="quote">

grimpeurcp · May 2007

It is 1/1024 as other have said. Those who say 50:50 are idiots.

We are talking about cascaded / cumulative probabilities.

Consider it as a finite state machine. If you get a head, you progress to the next state, if not you reset to state one and start again. To get the required result you must make ten state transitions, the probability of each is 0.5. The probability accumulates at each state transition 0.5^10 = 1/1024

For those interested, a technique based on this probability calculation, Maximum Likelihood Sequence Estimation, is used to perform error correction due to channel distortion in your mobile phone.

johndf · May 2007

Glad to see Natureboyz has gone quiet. He needs to read the question again.

Just in case you are there, Natureboyz, here is the question which I think you were answering. 'If a coin has already come up heads nine times in a row, what is the chance that it will come up heads next time?' This is totally different to the question which was asked.

If you really were answering the original question as asked, then you have no understanding of probability. But that puts you in the same class as Professor Roy Meadows, who understands nothing about probability, (well statistical independence anyway), yet gets women convicted because apparently none else in court understood this simple concept either.

As for the snooker question, the probability is zero, assuming that you can measure with perfect accuracy.

Mollie · May 2007

<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by DaveyL

The birthday one is a good one. I believe the "choose one from three, then have one wrong choice revealed to you" problem also comes up in the book "The Curious Incident of the Dog in the Nighttime" where the mathematical proof is also given. I could be thinking of another problem though.
<hr height="1" noshade id="quote"></blockquote id="quote">Good book. I've also seen both that and the birthdays one in "The Magical Maze" by Ian Stewart (I think).

maddog_2cp · May 2007

<blockquote id="quote">quote:<hr height="1" noshade id="quote">'If a coin has already come up heads nine times in a row, what is the chance that it will come up heads next time?'<hr height="1" noshade id="quote"></blockquote id="quote">

pay attention at the back please.

all answers are available to those who read the whole post

Drop bars are a historical accident...... discuss

dave5ncp · May 2007

It was all revealed on Desert Island Discs

 please pretend there's a horizontal line here. I couldnt work out how to put one in.
You stir my natural emotions

Unknown · May 2007

Actually, the proof of the "Monty Hall Problem" in The Curious incident of the Dog in the Nighttime is given in graphical form.

It's the only way I've ever been able to understand it. Cause I'm a bit thick, me.

Cheers,

Tim

http://vizarch.blogspot.com

John C. · May 2007

On a similar note (well not really)

'what is the air speed velocity of a swallow?'

http://www.ripon-loiterers.org.uk/index.asp

He who spins lasts longest

Mister Paul · May 2007

I'm starting to get worried now. I can feel people edging towards the keyboard with thoughts of jet planes and conveyor belts. Please don't. Natureboys would explode trying to figure it out.

__________________________________________________________
Road Safety Expert

Jaded · May 2007

Ask him on a Friday night then. [:D]

--
[Warning] This post may contain a baby elephant or traces of one

photojonny · May 2007

<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by John C.

On a similar note (well not really)

'what is the air speed velocity of a swallow?'
<hr height="1" noshade id="quote"></blockquote id="quote">

A European swallow?

where there's two wheels, there's a way....

mr_hippo · May 2007

Possibly an African one but African swallows are non-migratory.

http://bangkokhippo.blogspot.com/

Ex-XXL weigh-in 26/27 May: Update published: Monday 28 May

Neilums · May 2007

<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by John C.

On a similar note (well not really)

'what is the air speed velocity of a swallow?'

http://www.ripon-loiterers.org.uk/index.asp

He who spins lasts longest
<hr height="1" noshade id="quote"></blockquote id="quote">

Zero, if it's migratory.

frankblackcat · May 2007

I'm thinking of upgrading my tossing coin. Should I get a Shimano or Campagnolo?

maddog_2cp · May 2007

toss off

Drop bars are a historical accident...... discuss

John C. · May 2007

<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by photojonny

<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by John C.

On a similar note (well not really)

'what is the air speed velocity of a swallow?'
<hr height="1" noshade id="quote"></blockquote id="quote">

A European swallow?

where there's two wheels, there's a way....
<hr height="1" noshade id="quote"></blockquote id="quote">

African

http://www.ripon-loiterers.org.uk/index.asp

He who spins lasts longest

Unknown · May 2007

This is quite entertaining:

http://www.brainbashers.com/gameloader/ ... p?game=209

Magic, eh?

maddog_2cp · May 2007

now that's weird

Drop bars are a historical accident...... discuss

maddog_2cp · May 2007

I've just done 10 numbers and it guessed every one. Include random numbers from my phone book.

Drop bars are a historical accident...... discuss

oldwelshman · May 2007

Yeah right. So how many times you won the lottery jackpot?
The answer is as stated 1024 from 2 to the power of 10, simple.
<blockquote id="quote">quote:<hr height="1" noshade id="quote">Originally posted by cacbyname

When I was doing probability at school in Maths, I had an eccentric physics teacher at the same time who explained to us that all probabilities come down to a half - it can be a single coin toss, ten consecutive coin tosses, the odds of predicting the Grand National winner or of Elvis being found alive on the same day that aliens land in Trafalgar square. An event will either happen or it won't, hence the chance is always fifty:fifty.

For those who've had a sense of humour bypass operation, he advised us to stick to conventional theory that leads to answers like 1/1024 for exams and gambling.
<hr height="1" noshade id="quote"></blockquote id="quote">

Feel free to browse and donate:
http://www.justgiving.com/davidbethanmills
My winter and summer bike pics

http://oldwelshman.myphotoalbum.com

cacbyname · May 2007

Never won the lottery as I've never played it. I feel I pay enough tax already without making a voluntary contribution and I prefer to choose the beneficiaries of my charitable donations myself.

Sounds like your operation was a success at least [:)]

OT maths problem

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