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#1 2014-02-18 15:10:47

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Torpedos

Suppose that each torpedo has a 1/3 probability of sinking a ship, 1/3 probability of damaging it and 1/3 of missing it altogether. Moreover, 2 damaging shots will also sink the ship. What is  The probability that firing four torpedoes will sink the ship ?


'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 2014-02-18 18:45:11

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Torpedos

Hi,


"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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#3 2014-02-18 19:19:53

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

Re: Torpedos

Hi;


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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#4 2014-02-19 02:10:30

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Torpedos

Hi,

One more way for the general solution:


"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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#5 2014-02-19 02:44:09

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

Re: Torpedos

Hi;

Very good!


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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#6 2014-02-19 03:01:37

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Torpedos

That's good too!


"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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#7 2014-02-19 03:38:57

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

Re: Torpedos

Hi gAr;

Here is the ugly way!


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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#8 2014-02-19 04:11:35

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Torpedos

Computed using tree?


"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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#9 2014-02-19 04:13:30

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

Re: Torpedos

Used the multinomial distribution, then saw that it was easy to do by hand. Just enumerate the winning situations for 4 throws.


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 2014-02-19 04:21:27

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Torpedos

I see..


"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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#11 2014-02-19 04:27:27

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

Re: Torpedos

Hi;

Not the usual way I like to work. Casework is boring.


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 2014-02-19 04:40:01

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Torpedos

Yes, and recurrences are usually simple and small for these kind of problems.


"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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#13 2014-02-19 04:41:45

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

Re: Torpedos

Even if they are not, they tell things about the problem that the casework does not provide.


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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#14 2014-02-19 04:50:12

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Torpedos

That's true.


"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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#15 2014-02-19 04:55:19

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

Re: Torpedos

How is everything been?


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 2014-02-19 05:12:14

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Torpedos

Mostly good.


"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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#17 2014-02-19 05:21:57

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

Re: Torpedos

What have you been doing?


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

#18 2014-02-19 05:40:41

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Torpedos

Just math!


"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."

Offline

#19 2014-02-19 05:47:48

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

Re: Torpedos

I have been sidetracked with other things but maybe I can get some in today.


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 2014-02-19 06:04:12

gAr
Member
Registered: 2011-01-09
Posts: 3,482

Re: Torpedos

Math and programming are great fun, but too bad there are some folks who don't know what a computer does and ask me about it. And if I say math, they understand it as arithmetic!


"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."

Offline

#21 2014-02-19 06:06:20

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

Re: Torpedos

Most people studying math do not associate computers and mathematics.


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 2014-02-19 15:31:42

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 24,974
Website

Re: Torpedos

bobbym wrote:

Hi gAr;

Here is the ugly way!

Explain this one, first


'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

#23 2014-02-19 15:58:12

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

Re: Torpedos

This is a casework solution. First, do you have a simulation answer and if possible a direct answer by computer?

Here is one way M can assist you. M has the most powerful probability and statistics routines in existence already built in.

dd = MultinomialDistribution[4, {1/3, 1/3, 1/3}];

Probability[s > 0, {s, d, m} \[Distributed] dd] + Probability[d > 1 && s == 0, {s, d, m} \[Distributed] dd]

We label the three outcomes s for sink, d for damage and m for miss. Let's count them up by hand...

But first please provide me with a simulation answer in M.


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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#24 2014-02-20 03:25:45

John E. Franklin
Member
Registered: 2005-08-29
Posts: 3,588

Re: Torpedos

How come you can't hit the ship 4 times in a row under water, or 2 hits and 2 damages?

Last edited by John E. Franklin (2014-02-20 03:26:45)


igloo myrtilles fourmis

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#25 2014-02-20 03:28:07

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

Re: Torpedos

Hi John;

Four times in a row is (1 / 3)^4 = 1 / 81


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

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