OT maths problem

bonescp · May 2007

what are the odds of tossing a coin and getting 10 heads in row,
this is a friendly arguement at work someone said it was 50 50 but this didnt sound right to me .ive looked on the maths forums but this only got more confussing.

john

Unknown · May 2007

1 in 1024 by recockoning.

The chance each time is one in two = 0.5. Then you have ten separate independent trials so the chance of all being heads is 0.5 to the power 10 = 1/1024.

natureboyz · May 2007

50/50
No other factors come into it.

Unknown · May 2007

Bones,

Every time you toss a coin, the probability of getting a 'Head' P(H)=0.5. Similarly the probability of getting a 'Tail' , P(T)=0.5

The probability of getting 10 Heads in a row is P(H)x P(H)x P(H)x P(H)x P(H)x P(H)x P(H)x P(H)x P(H)x P(H)

which is 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 x 0.5 = 0.0009765635 or 1 in 1024

Apologies I am a very sad former statistician!

_____________________________________________________________________
Be nice to grumpy old men (or else)

gordycp · May 2007

pme is correct.
You could "prove" it by writing out all 1024 combinations;

HHHHHHHHHH
HHHHHHHHHT
HHHHHHHHTH
HHHHHHHTHH

and so on.
Enjoy!

Two sheds · May 2007

Just to add to the confusion...your friend might be talking about conditional probability. If you've tossed a coin and got 9 heads in a row, then the odds of making it 10 in a row are 50:50. The coin has no memory.

Put a hump in your back
Shake your sacroiliac
And ride on

Mister Paul · May 2007

natureboy is wrong.

Look at it with two. You get the following possible combinations-

HH
HT
TH
TT

So you've got a 1 in 4 chance of getting two consecutive heads. Keep going like this and you get the 1/1024 with 10 throws.

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Road Safety Expert

natureboyz · May 2007

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

natureboy is wrong.

Look at it with two. You get the following possible combinations-

HH
HT
TH
TT

So you've got a 1 in 4 chance of getting two consecutive heads. Keep going like this and you get the 1/1024 with 10 throws.

__________________________________________________________
Road Safety Expert
<hr height="1" noshade id="quote"></blockquote id="quote">
He asked about one not two so your example is meaningless.

Mister Paul · May 2007

C'mon Mildred. You could at least concede gracefully, rather than making yourself look more dense.

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Road Safety Expert

craigwend · May 2007

http://en.wikipedia.org/wiki/Gambler's_fallacy

Space to rent '......................................................' reasonable offers only.

http://s156.photobucket.com/albums/t6/craigwend

natureboyz · May 2007

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

C'mon Mildred. You could at least concede gracefully, rather than making yourself look more dense.

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Road Safety Expert
<hr height="1" noshade id="quote"></blockquote id="quote">

The fact that it is you who is the dense one conveniently escapes you attention DUMBO .

mr_hippo · May 2007

I thought it might be one of those delicious problems that would make me think but sadly I am wrong! Answer: 50/50

http://bangkokhippo.blogspot.com/

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

Jaded · May 2007

It isn't 50:50.

Not in the way the question was asked by the OP.

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nun · May 2007

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

1 in 1024 by recockoning.

The chance each time is one in two = 0.5. Then you have ten separate independent trials so the chance of all being heads is 0.5 to the power 10 = 1/1024.
<hr height="1" noshade id="quote"></blockquote id="quote">

Give that man a GCSE in maths. He's right.

A good one is to ask "After a snooker break, what's the probability that the snooker balls come to rest in exactly the same positions as before the break"?

Bloke on a bikecp · May 2007

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

what are the odds of tossing a coin and getting 10 heads in row,
<hr height="1" noshade id="quote"></blockquote id="quote">
Those of you that think that the odds are 50/50: I'd love to meet you in a pub. Tell you what, I'll even give you double the "odds". If you can throw 10 heads in a row, I'll give you œ20. If you can't, you pay me œ10. [:D]

I think that some of you must have read the OP's question as "If a coin has been tossed 9 times and come down as heads each time, what are the odds of the tenth throw being heads?"
That would indeed be evens. But that wasn't the question, was it?

--
Basil W Brush

Mister Paul · May 2007

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

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

C'mon Mildred. You could at least concede gracefully, rather than making yourself look more dense.

__________________________________________________________
Road Safety Expert
<hr height="1" noshade id="quote"></blockquote id="quote">

The fact that it is you who is the dense one conveniently escapes you attention DUMBO .
<hr height="1" noshade id="quote"></blockquote id="quote">

Toss two coins. Toss the same coin twice. Same probabilities.

Get it yet?

__________________________________________________________
Road Safety Expert

natureboyz · May 2007

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

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

1 in 1024 by recockoning.

The chance each time is one in two = 0.5. Then you have ten separate independent trials so the chance of all being heads is 0.5 to the power 10 = 1/1024.
<hr height="1" noshade id="quote"></blockquote id="quote">

Give that man a GCSE in maths. He's right.

A good one is to ask "After a snooker break, what's the probability that the snooker balls come to rest in exactly the same positions as before the break"?

<hr height="1" noshade id="quote"></blockquote id="quote">

No, he isn't.
Each of the two possible outcomes has equal probability no matter how many times the coin has been flipped previously and no matter what the result.

Unknown · May 2007

I have A level maths, oooohh!

natureboyz · May 2007

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

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

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

C'mon Mildred. You could at least concede gracefully, rather than making yourself look more dense.

__________________________________________________________
Road Safety Expert
<hr height="1" noshade id="quote"></blockquote id="quote">

The fact that it is you who is the dense one conveniently escapes you attention DUMBO .
<hr height="1" noshade id="quote"></blockquote id="quote">

Toss two coins. Toss the same coin twice. Same probabilities.

Get it yet?

__________________________________________________________
Road Safety Expert
<hr height="1" noshade id="quote"></blockquote id="quote">

Don't be stupid over here as well .Save it for Campaign

Bloke on a bikecp · May 2007

<snigger>
Natureboyz, please read the original post again.

--
Basil W Brush

natureboyz · May 2007

I have read it thank you sniggerer.

Bloke on a bikecp · May 2007

OK [:D][:D][:D]

--
Basil W Brush

Jaded · May 2007

<snigger> [:D]

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

natureboyz · May 2007

How old are you Miss Goody ?
Five ,six maybe .

Johnpsanderson · May 2007

Can ya tell it's Friday evening? Some people have had a BAD week at work....

It's ALL about the bike.

andrewgturnbull · May 2007

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

I have read it thank you sniggerer.
<hr height="1" noshade id="quote"></blockquote id="quote">

Hi there.

natureboyz - why don't you test your hypothesis and prove the sniggers wrong?

Toss a coin 10 times in a row and write down the results. If you don't get ten heads in a row, then try again - using your argument you'll probably crack it the second time.

I'd be genuinely interested to know how you got on - can you let us know?

Cheers, Andy

http://www.stirlingtri.co.uk

Garybee · May 2007

Natureboyz, you are correct for any indivudual throw, regardless of the number of throws before. But the question was regarding the result of numerous throws. As a more practical example, have you ever bet on an accumulator at the bookies? If what you are saying was correct, they would lose a lot of money.

Hypocrisy is only a bad thing in other people.

andrewgturnbull · May 2007

On a slightly different topic. natureboyz - have you ever met Monty Hall?

http://www.stirlingtri.co.uk

Jaded · May 2007

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

How old are you Miss Goody ?
Five ,six maybe .
<hr height="1" noshade id="quote"></blockquote id="quote">

oh, paganini.

What class. [:D][:D][:D]

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

Mister Paul · May 2007

Natureboyz. You're getting mixed up.

Toss a coin ten times. Each time you have a 50% change of heads. Now, that's where you've stopped thinking.

Now, toss it twice. The possible outcomes are

Head head
head tails
tails head
tails tails

So with 2 throws, you have a 1 in 4 chance of getting both heads. Not a 1 in 2, as you think.

Now with three throws-

HHH
HHT
HTT
HTH
THH
THT
TTH
TTT

So after three throws there are 8 possible outcomes. Only one is all heads, so that's a one in 8 chance. Not a 1 in 2, as you think.

And so on, all the way up to ten throws.

That's about as simple as it can be explained. Do you still not understand?

__________________________________________________________
Road Safety Expert

nun · May 2007

Originally posted by natureboyz

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

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

1 in 1024 by recockoning.

The chance each time is one in two = 0.5. Then you have ten separate independent trials so the chance of all being heads is 0.5 to the power 10 = 1/1024.
<hr height="1" noshade id="quote"></blockquote id="quote">

Give that man a GCSE in maths. He's right.

A good one is to ask "After a snooker break, what's the probability that the snooker balls come to rest in exactly the same positions as before the break"?

<hr height="1" noshade id="quote"></blockquote id="quote">

So nobody wants to answer the snooker question?

OT maths problem

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