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## #1 2013-04-03 03:44:11

concept
Member
Registered: 2013-04-03
Posts: 1

### Expected number of questions to win a game

Let, a person is taking part in a quiz competition.
For each questions in the quiz, there are 3 answers, and for each correct answer he gets 1 point.
When he gets 5 points, he wins the game.
But, if he gives 2 consecutive wrong answers, then his points resets to zero (i.e. if his score is now 4 and he gives 2 wrong answers, then his score resets to 0).

My question is, on an average how much questions he needs to answer to win the game?

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## #2 2013-04-03 03:46:48

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

Hi concept;

Welcome to the forum.

Before I can answer I would like to know what course you are taking. Does a Markov chain sound familiar to you? Would that be an acceptable answer?

Also, I see that you have posted this same question on another forum. Both of us working on the same problem is a waste of time for the volunteers at both forums.

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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## #3 2013-04-03 06:24:38

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### Re: Expected number of questions to win a game

Linear algebra's applications on probability! And bobbym, how can we evaluate the matrices without wolfram?

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## #4 2013-04-03 06:34:34

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

I will not be able to answer that question until I am done constructing the matrix. Offhand I would say that doing any but the smallest Markov chains by hand is foolish.

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 2013-04-03 11:40:38

ShivamS
Member
Registered: 2011-02-07
Posts: 3,648

### Re: Expected number of questions to win a game

Take the city and suburb matrix from the other thread. Like it may be foolish, but good to know the fundamentals.

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## #6 2013-04-03 13:37:47

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

This matrix is bit bigger than that one. I have the answer I just need another way that agrees with that answer. Anyways, it will all appear right here in the future.

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 2013-04-03 13:47:11

shivamfhutfft
Guest

### Re: Expected number of questions to win a game

I get Howe to drawcthe initial state and transition matrices evaluating I'ds an issue and on phone do bad gtammar

## #8 2013-04-03 23:24:25

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

Hi concept;

Using the standard methods of dealing with an absorbing Markov matrix I get:

This is the expected number of questions needed to win the game.

This agrees well with the answer supplied by a simulation.

Concept;

You have posted this question all over the internet and I have answered it in violation of our homework code.

http://www.mathisfunforum.com/viewtopic.php?id=14654

When I do this, I do it once just in case you are in earnest need of help. In the future I will give you the same answer all the other forums did. You must do your own homework.

Mathematics is not something you just have to get passed on your way to some career in hotel management, it is an important field in itself. Probably the most important. I strongly urge that you do not take shortcuts in life. No matter what job you end up in hard work is required. Your hard work not mine. I will expect in the future that when you post homework you at least try to do it and of course show your tries.

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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## #9 2013-04-03 23:57:51

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Expected number of questions to win a game

Hi bobbym,

Got the same answer, but did it with 2 states less.
You may eliminate r0w1 and w2 and use start state instead.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #10 2013-04-04 00:00:55

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

Hi gAr;

You always get less states than I do. It is a gift.

How are you?

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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## #11 2013-04-04 00:14:38

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Expected number of questions to win a game

Hi bobbym,

I was trying to make sense of the probability it was giving for 6 questions and the answer mentioned in the other forum, which are 13/729 and 10/729.
Then realized that this matrix adds the previous probabilities as well.
Doing something with markov model after quite a long time!

Anyway, I'm fine, how are you?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #12 2013-04-04 00:17:32

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

I have been working hard on many problems, some I got some I did not.

I am looking at a new series idea for problems of this type but no luck yet. Added some stuff at the OEIS.

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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## #13 2013-04-04 00:23:06

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Expected number of questions to win a game

Which are those problems?

Perhaps we may maintain a separate thread for unsolved problems in this site? Or something to highlight that it's unsolved?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #14 2013-04-04 00:25:13

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

That would be a good idea.

anonimnystefy and I were trying to come up with a closed form for all his columns that come from his solution to Matt's dice 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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## #15 2013-04-04 00:32:49

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Expected number of questions to win a game

Oh, that! I think I tried really hard that day, but why that matrix?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #16 2013-04-04 00:35:20

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

I do not know, he asked for some help with it and we got the first column, a really nice and simple form but all others would not conform.

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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## #17 2013-04-04 00:44:52

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Expected number of questions to win a game

I too would like to know an answer, but some problems beat us, sadly!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #18 2013-04-04 00:48:47

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

I am afraid that if we work on a lot of problems we are going to have a big collection of unsolved ones. I know I do. But at least we have fun.

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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## #19 2013-04-04 00:52:25

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Expected number of questions to win a game

That's true! Enjoying the process is more important than desiring for a solution.

Taking a break, see you later..

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #20 2013-04-04 00:54:47

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

Hi gAr;

Thanks for coming in. See you later.

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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## #21 2013-04-04 01:26:58

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Expected number of questions to win a game

Hi bobbym,

Added some stuff at the OEIS.

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #22 2013-04-04 01:31:48

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

Hi gAr;

Yes, 2 or 3 additions and a new sequence.

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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## #23 2013-04-04 01:39:20

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Expected number of questions to win a game

That's nice! May I know which are those?

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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## #24 2013-04-04 01:42:14

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

### Re: Expected number of questions to win a game

Oh I am sorry, check under [removed by administrator]

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

## #25 2013-04-04 01:48:31

gAr
Member
Registered: 2011-01-09
Posts: 3,479

### Re: Expected number of questions to win a game

Hi bobbym,

Went there, good ones!

"Believe nothing, no matter where you read it, or who said it, no matter if I have said it, unless it agrees with your own reason and your own common sense"  - Buddha?

"Data! Data! Data!" he cried impatiently. "I can't make bricks without clay."

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