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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,192

This certain math instructor was telling an anecdote about an admiral and his subordinates trying to figure out how to be sure to destroy an enemy target using a certain missile. Now the admiral explains to his men that the missile has a 1/3 chance of destroying the target. He mistakenly states therefore it will take 3 missiles to definitely destroy the target. One of the subordinates is asked if that is correct. He reasons that each missile has a 1/3 chance so he punches into his calculator .3333333333+.3333333333+.3333333333=.9999999999. This he correctly states is slightly less than 1 so it will take a little bit more than 3 missiles to definitely destroy the target.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

An example of Military Intelligence?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**Ubergeek****Member**- Registered: 2009-07-14
- Posts: 205

You meant he **in**correctly states right?

"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,192

Hi Ubergeek;

Since these are terminating decimals he is right about .3333333333+.3333333333+.3333333333=.9999999999 < 1

*Last edited by bobbym (2009-08-03 11:23:05)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,608

So long as they are terminating decimals.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,192

Hi;

Definitely, his mistake is that he truncated 1/3 to a terminating decimal. Instead of punching in 1/3 in his calc (many scientific calcs when adding 1/3, 3 times will get 1 as the answer) he punched in .3333333333

I think the math instructor is trying to say that the subordinate thinks .3333333333 = 1/3 when .3333333333... = 1/3

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.** **A number by itself is useful, but it is far more useful to know how accurate or certain that number is.**

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**Ubergeek****Member**- Registered: 2009-07-14
- Posts: 205

bobbym wrote:

Hi;I think the math instructor is trying to say that the subordinate thinks .3333333333 = 1/3 when .3333333333... = 1/3

I think it may be so. Either way, isn't the difference way to little to take another missile to destroy the target? I mean, you don't have to pulverize **it all**, the difference of 0.9999999999 to 1 can't mean anything relevant.

"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,192

Hi Ubergeek;

The problem now becomes that the admiral and the subordinate believe you can a add the probabilities up. It's simple to prove that this is nonsense 4 * 1/3 = 4/3 so 4 missiles gives you a probability of 4/3 of destroying the target? Probablities can not exceed 1 and 4/3 is bigger than 1.

In actuality, firing 3 missiles only gives you a probability of 1-(2/3)^3 ≈ .7037 or about a 70% chance that you have destroyed the target. Their analysis is foolish because no amount of missiles can guarantee that the target is destroyed.

*Last edited by bobbym (2009-08-03 19:27:39)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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**Ubergeek****Member**- Registered: 2009-07-14
- Posts: 205

bobbym wrote:

Hi Ubergeek;

The problem now becomes that the admiral and the subordinate believe you can a add the probabilities up. It's simple to prove that this is nonsense 4 * 1/3 = 4/3 so 4 missiles gives you a probability of 4/3 of destroying the target? Probablities can not exceed 1 and 4/3 is bigger than 1.

In actuality, firing 3 missiles only gives you a probability of 1-(2/3)^3 ≈ .7037 or about a 70% chance that you have destroyed the target. Their analysis is foolish because no amount of missiles can guarantee that the target is destroyed.

Lol, that's true. I got so caugh up in the decimal thing I didn't realized the joke was on the probability. Thanks for clarifying bobbym.

"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true."

Bertrand Russell

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 104,192

Hi Ubergeek;

The joke is really on the people who live in that country and are trusting there navy to defend them.

*Last edited by bobbym (2009-08-05 06:25:31)*

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.**

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