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Another problem for you not to solve :)


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There is a drunk man standing on the number 0. The man stumbles back and forth, and he has a 50% chance of moving backward (0 to -1 ect) on each move and a 50% chance of moving forward on each move. Prove that after an infinite number of moves, the probability of the man reaching 1 is 100%.

 

 

:D

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YT2095 said in post # :

you`ve just given the answer away in the last sentence :)

when dealing with infinates you therefore make anything and everything possible. :)

 

got anything harder? LOL :)

 

That's not proof.

 

It's very similar to a problem I did on a STEP paper recently.

 

What you've got is a system where it's a 1/2 chance of moving forwards, and a 1/2 chance of moving backwards. When you move backwards, 1/2 of the time you move forwards yadda yadda yadda infinite sum of a geometric series where a = 1 and r = 1/2.

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mrl,

I lock you in jail, I pick a whole number between 1 and infinity, if you can guess this number, I will let you out to be free.

then I change the rules, I say it can be any HALF number aswell!

am I making it twice as hard for you to get out of jail???

 

as I said. when dealing with INFINATES, all outcomes are garaunteed 100% :)

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YT2095 said in post # :

mrl,

I lock you in jail, I pick a whole number between 1 and infinity, if you can guess this number, I will let you out to be free.

then I change the rules, I say it can be any HALF number aswell!

am I making it twice as hard for you to get out of jail???

 

as I said. when dealing with INFINATES, all outcomes are garaunteed 100% :)

 

That's not a mathematical proof though. It's just stating that it's infinite therefore it must happen. Which is what I commented about above.

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What you've got is a system where it's a 1/2 chance of moving forwards, and a 1/2 chance of moving backwards. When you move backwards, 1/2 of the time you move forwards yadda yadda yadda infinite sum of a geometric series where a = 1 and r = 1/2.

 

Actually, that is incorrect. Although the probability of reaching 1 after a single move is 1/2, the probability of reaching 1 in three moves is 5/8 (1/2 will get there on the first move, and only 1/8 will get there on the third move).

 

The sum you suggest looks like: 1/2 + 1/4 + 1/8... = 1.

 

What we actually are seeing is: 1/2 + 1/8

 

 

You are going to have to explain exactly where your terms are comming from if you use the series you suggested.

 

when dealing with infinates you therefore make anything and everything possible.

 

That just isn't true. It isn't possible for the man to continue moving back anf forth between 0 and -1 for an infinite number of moves. The probability of this occuring approaches 0% as the number of moves approach infinity. Hence, your statement is false. :)

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BrainMan said in post # :

You are going to have to explain exactly where your terms are comming from if you use the series you suggested.

 

I couldn't really be bothered to sort it out, because it takes (with full working) a reasonable amount of time, and it always comes down to an infinite geometric series.

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I also couldn`t be bothered trying to word it any better (I`m not that great in that department).

it`s just when INFINATES (as in number of tries) all combinations are performed, including him actualy being on `1` at some time).

 

a million monkeys with a million typwriters and all that stuff :)

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The pattern is the following:

 

1st step: P(1) = 1/2, P(-1) = 1/2

 

2nd step: P(2)= 1/4, P(0) = 1/4 + 1/4 = 1/2, P(-2) = 1/4

 

The probability to reach 0 in the 2nd step is equal to the probablity of being at 2 and making a step backward (1/2 * 1/2 = 1/4) and the probability of being at -1 and making a step forward (1/2 * 1/2 = 1/4).

 

3rd step: P(3) = 1/8, P(1) = 1/8 + 1/4, P(-1) = 1/4 + 1/8, P(-3) = 1/8

 

The probability of reaching 1 in step 3 is P(3) + P(1) = 1/2

 

If P(s, n) denotes the probability of accessing point n at step s, then we have:

 

P(s, n) = 1/2 * P(s-1, n-1) + 1/2 * P(s-1, n+1)

 

You must compute the limit of the sum of all P(s, n), where n>=1 (that's what it means to "reach 1"), for s tending to infinity.

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  • 7 years later...
  • 2 months later...

This is a topic change. I am planning a book. I ask a lottery purchaser this: "Okay, say the state takes in 100 million dollars for a lottery. It keeps 50 million dollars. That is ok with you?" They nod. "So it is ok for the state to do that- you know they keep part of it- you knew that?'' yes, they say. "So when you buy a lottery ticket and spend $1, then 50 cents goes to the state, right?"

 

They don't get it. Goes right over their heads. Our lives are run by media and politicians that hate math. Isn't this really arithmetic? Maybe all of 8th grade arithmetic? This is some huge disconnect. The two camps have a gulf as wide as an ocean between. Why are we supposed to couch things in words? Why can't they speak in at least rudimentary level of our language.

 

It isn't an improved education needed. This is some kind of deep type of block. Why? Why? Why?

 

As an aside- does anyone here bet the lottery?

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This is a topic change. I am planning a book. I ask a lottery purchaser this: "Okay, say the state takes in 100 million dollars for a lottery. It keeps 50 million dollars. That is ok with you?" They nod. "So it is ok for the state to do that- you know they keep part of it- you knew that?'' yes, they say. "So when you buy a lottery ticket and spend $1, then 50 cents goes to the state, right?"

 

They don't get it. Goes right over their heads. Our lives are run by media and politicians that hate math. Isn't this really arithmetic? Maybe all of 8th grade arithmetic? This is some huge disconnect. The two camps have a gulf as wide as an ocean between. Why are we supposed to couch things in words? Why can't they speak in at least rudimentary level of our language.

 

It isn't an improved education needed. This is some kind of deep type of block. Why? Why? Why?

 

As an aside- does anyone here bet the lottery?

I bet on the lottery 50% of the time - that way I get my money's worth :rolleyes:

 

Chris

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