Math Is Fun Forum
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#1 2013-03-25 21:46:31
Another coin problem
You toss 25 coins.
What is the expected number of consecutive pair of heads?
Clarfication: for example, in a series of 6 coins if the result is HHTHHH then the number of consecutive pair of heads is 3
The answer is 6 according to an experiment......
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#2 2013-03-25 21:48:32
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Another coin problem
The actual answer is 24*1/4=6 as well.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
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#3 2013-03-25 21:59:10
Re: Another coin problem
Hmm .... How to do this?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#4 2013-03-25 22:33:41
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
Hi;
You use the linearity of expectation.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#5 2013-03-25 22:35:57
Re: Another coin problem
But I do not know about it! 
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#6 2013-03-25 22:37:38
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
Hi;
Okay, I will tell you what I know and please pay close attention to my signature.
Let Xi = 1 if the ith and (i+1)th coins are both heads, 0 otherwise, for i= 1,2,...,24.
E(Xi) = (1/2)(1/2) = 1/4.
Then the expected number of matches is
E(number of adj pairs) = 24 * (1/4) = 6.
Here we have used the theorem that E(X+Y) = E(X) +E(Y), which is true even if X and Y are not independent.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#7 2013-03-25 22:52:23
Re: Another coin problem
What won't you tell those fools?
That explanation went away tangentially over my head.
What is this Xi?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#8 2013-03-25 22:54:47
Re: Another coin problem
One minute, I went to the restroom and thought about it.
It seems I got the idea now
The probability that a coin and its next coin both are H is (1/4)
And as there are 24 coins (since there is no coin after the 25th), the Expected number of consecutive pair of heads is (1/4)*24
Have I got it correct?
Anyway whats xi?
Last edited by Agnishom (2013-03-25 22:57:25)
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#9 2013-03-25 22:56:10
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
What won't you tell those fools?
Hey, that is pretty funny!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#10 2013-03-25 22:58:46
Re: Another coin problem
Please see #8
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#11 2013-03-25 23:07:41
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
That is the idea! You can multiply them because of the linearity of expectation.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#12 2013-03-25 23:09:19
Re: Another coin problem
What does that mean?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#13 2013-03-25 23:12:46
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
When you are multiplying by 24 you are actually adding 24 things up.
E(x+y) = E(x)+E(y)
E(x+y+z)=E(x)+E(y)+E(z)
.
.
.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#14 2013-03-25 23:22:08
Re: Another coin problem
Yay got it
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#15 2013-03-25 23:23:25
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
You are a very clever person.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#16 2013-03-25 23:29:26
Re: Another coin problem
Are we still on the new s erver?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#17 2013-03-25 23:30:02
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
Yes, I believe so.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#18 2013-03-25 23:50:22
Re: Another coin problem
Hope you have already figured out, but in case you haven't : my exams just ended on March 22, 2013 1:35 PM IST
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#19 2013-03-25 23:55:57
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
How did you do?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#20 2013-03-26 00:02:48
Re: Another coin problem
Everything was okay except maths.
I am also afraid about Nky
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#21 2013-03-26 00:03:42
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
What are you afraid of and why was math a problem?
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
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#22 2013-03-26 00:14:28
Re: Another coin problem
Math was a problem because:
1. We had to finish a 90 marks paper within 3 hours. Which is lengthy enough for maths.
2. I have a tendency to make silly mistakes which are further enhanced by point 1. as I didn't have time to revise the paper
3. I may have forgotten to do a trivial (or a nontrivial) in my paper.
4. I could not solve a problem, which carried four marks.
Moreover, everyone expects me to do extremely good in math
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
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#23 2013-03-26 00:17:16
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
Sounds like a lot of pressure. You need a vacation.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline
#24 2013-03-26 00:22:15
Re: Another coin problem
I have got a vacation.
The results of the exams are on 11th April and our new sessions start from the 12th
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#25 2013-03-26 00:23:48
- bobbym
- bumpkin
- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 109,606
Re: Another coin problem
Oh, very good. I am being called away to do a chore. See you in a bit.
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.
Offline