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Paradoxes


pureprayer

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I found this one lets see if anyone can solve it:

 

 

 

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

 

 

 

Yes. You have a 1/3 chance of getting it in the 1st place, and a 1/2 after the 1st door. However, once he asks, that changes everything (aka variable oods). If you say yes, ill change, you'll have a 66% chance of winnning.

 

 

 

Cookies to who figure outs what thats from :XD:

 

 

 

you arent improving your odds by changing doors

 

 

 

at first pick each choice has 33% chance of being "correct"

 

 

 

if one door is revealed then each of the remaining two doors has 50% chance of being correct. The door you selected is equal to the door you could change to so it isnt an improvement.

 

Check again.

 

 

 

You have a 1/3 chance of a car and 2/3 chance of a goat if you dont switch.

 

 

 

But if you do pick the 66% chance of a goat and the host opens the other goat door and you switch you have a 66% chance of a car.

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Is the answer to this question no?

 

You have a 33% chance if you dont switch and a 66% if you do.

 

You see, I didn't quote you, because I wasn't referring to you post.

 

Normally when people don't quote other people they ARE referring to the post above them.

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Is the answer to this question no?

 

You have a 33% chance if you dont switch and a 66% if you do.

 

You see, I didn't quote you, because I wasn't referring to you post.

 

Normally when people don't quote other people they ARE referring to the post above them.

 

He was stating his own paradox, it's like: "Your mission is to not accept the mission. Do you accept?"

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what came first the chicken or the egg??? (yes, there is an actual answer that makes sense)

 

 

 

The egg because of evolution? A chicken can evolve from one thing, but an egg is still an egg throughout evolution.

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what came first the chicken or the egg??? (yes, there is an actual answer that makes sense)

 

Chicken?

 

 

 

Is the answer to this question no?

 

You have a 33% chance if you dont switch and a 66% if you do.

 

You see, I didn't quote you, because I wasn't referring to you post.

 

Normally when people don't quote other people they ARE referring to the post above them.

 

He was stating his own paradox, it's like: "Your mission is to not accept the mission. Do you accept?"

 

I get it now #-o

 

 

 

Sorry Jem

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I found this one lets see if anyone can solve it:

 

 

 

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

 

 

 

Yes. You have a 1/3 chance of getting it in the 1st place, and a 1/2 after the 1st door. However, once he asks, that changes everything (aka variable oods). If you say yes, ill change, you'll have a 66% chance of winnning.

 

 

 

Cookies to who figure outs what thats from :XD:

 

I am not sure where you got i from, I heard it from Numb3rs when we watched every episode in math last year. Cookie Please

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I found this one lets see if anyone can solve it:

 

 

 

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

 

 

 

Yes. You have a 1/3 chance of getting it in the 1st place, and a 1/2 after the 1st door. However, once he asks, that changes everything (aka variable oods). If you say yes, ill change, you'll have a 66% chance of winnning.

 

I'm guessing I'm missing something but wouldn't it be a 50% chance for door 1 or door 2?

 

 

 

 

 

Onto another Paradox, someone mentioned something similar but this is different:

 

 

 

There is a running race between 2 people. Person A gets a head start and when he reaches 100m, Person B can run. But Person B runs 10 times faster than Person A. Now say that they keep running at a constant speed, will Person B ever catch up to Person A?

 

 

 

The answer is no, because by the time Person B runs 100m, Person A will be 10m ahead, and when Person B runs those 10m, Person A will be 1m ahead and so on and so on.

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I found this one lets see if anyone can solve it:

 

 

 

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

 

 

 

Yes. You have a 1/3 chance of getting it in the 1st place, and a 1/2 after the 1st door. However, once he asks, that changes everything (aka variable oods). If you say yes, ill change, you'll have a 66% chance of winnning.

 

I'm guessing I'm missing something but wouldn't it be a 50% chance for door 1 or door 2?

 

 

 

 

 

Onto another Paradox, someone mentioned something similar but this is different:

 

 

 

There is a running race between 2 people. Person A gets a head start and when he reaches 100m, Person B can run. But Person B runs 10 times faster than Person A. Now say that they keep running at a constant speed, will Person B ever catch up to Person A?

 

 

 

The answer is no, because by the time Person B runs 100m, Person A will be 10m ahead, and when Person B runs those 10m, Person A will be 1m ahead and so on and so on.

 

 

 

That doesn't really work.

 

 

 

Person B will eventually overtake Person A since Person B is running faster.

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I found this one lets see if anyone can solve it:

 

 

 

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

 

 

 

Let's see...

 

 

 

The original probability of getting a car is 1/3, or 33%.

 

The original probability of getting a goat is 2/3, or 66%.

 

 

 

When door three is opened and it has a goat, the game is changed and we have a new set of probabilities:

 

The new probability of getting a car is 1/2, or 50%.

 

The new probability of getting a goat is 1/2, or 50%.

 

 

 

I'd say there is no advantage to switching from the original choice of door 1.

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I found this one lets see if anyone can solve it:

 

 

 

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

 

 

 

Let's see...

 

 

 

The original probability of getting a car is 1/3, or 33%.

 

The original probability of getting a goat is 2/3, or 66%.

 

 

 

When door three is opened and it has a goat, the game is changed and we have a new set of probabilities:

 

The new probability of getting a car is 1/2, or 50%.

 

The new probability of getting a goat is 1/2, or 50%.

 

 

 

I'd say there is no advantage to switching from the original choice of door 1.

 

 

 

 

 

According to 21 switching doors apparently does have some sort of benefit, can't remember what though.

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As a point of general interest you can't divide by zero. Any number divided by zero does NOT = zero. A calculator will normally give: error, divide by zero error, or undefined (the latter being to generaly excepted answer). Zero is nothing, and you can't divide anything by nothing, you can't even divide nothign by nothing. It dosen't equal infinity, it is simply undefined. And thats from a mathmatical system that solved how to square root a negative (or any even root).

 

 

 

I like the one about half distances, and because an object must always travel half the distance to it's destination, it will never get there because everytime it gets half way, there is a new halfway. Unfortunatly thats more bad logic and lack of calulus (which actualy can be used to divide by zero, its called finding tanget lines) than anything else, and it is quite obviusly false.

 

 

 

There is also one about at any single point in time, nothing can move, since all movement is essentialy a distance for a given time interval (or a derivitive of that function such as acceleration, jerk and snap). If the given time interval is zero, then there can't be movement becuase we are back at tehhe whole dividing by zero thing. Acording to teh original idea, movement is immpossible becuase time is an infinate series of instantaneous points and there can be no movement at an instantaneous point in time.

 

 

 

Other than bad logic, infinity offers a few good one. First off, due to the nature of the concept of infinity, all infinitys are equal. There are also infinate numbers. Now consider this:

 

- The number of even numbers = infinity and the number of odd numbers = infinity so the number of even numbers = the number of odd numbers. Strait forward so far?

 

- There are an infinate number of numbers, so the # of even numbers = # of odd numbers = infinty = number of numbers

 

- There are an infinate number of numbers so there are also in infinate ammount of prime numbers therfore the # of numbers = the # of prime numbers. Now think about that one. To our minds, we know that there are definatly more numbers that there are prime numbers, especialy considering that numbers incluses prime (plus a whole lot more). Still, becuase of how all infinitys are equal, the statement stands.

 

 

 

Not really a paradox, but I realy like the mobius strip (just wikipedia it if you don't know what it is or how to make one). Everytime I make one and trace a line on it, it just blows my mind all over again. How can a 1 sided object (minus the edges) exist in 3D space? Even if you count edges, which adds 2 sides, you only have 3 sides. 3 sides is good enough you say? How about you go find me a D3 (3 sided die).

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0/0 = 0

 

:wall: The fail posts just keep getting worse.

 

 

 

I don't know any paradoxes, but here's a math riddle:

 

If you have 36 cigarette buds, and if you can make 1 new cigarette by combining 6 buds together, how many extra cigarettes can you make?

 

Define "extra".

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Let's see...

 

 

 

The original probability of getting a car is 1/3, or 33%.

 

The original probability of getting a goat is 2/3, or 66%.

 

 

 

When door three is opened and it has a goat, the game is changed and we have a new set of probabilities:

 

The new probability of getting a car is 1/2, or 50%.

 

The new probability of getting a goat is 1/2, or 50%.

 

 

 

I'd say there is no advantage to switching from the original choice of door 1.

It might seem awkward, but there is an advantage in switching. Look at all six possible outcomes (all of which have the same possibility):

 

You pick the car. You keep it.

 

You pick the car. You switch, and get the goat.

 

You pick Goat 1. You keep it.

 

You pick Goat 1. You switch and get the car.

 

You pick Goat 2. You keep it.

 

You pick Goat 2. You switch and get the car.

 

 

 

So, with the "switching" strategy, you'll get the car 2/3 of the time.

 

 

 

Anyway, this is no paradox, just counter-intuitive maths.

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The Spice Girls Paradox

 

[hide=]If you wanna be my lover, you gotta get with my friends... but wouldn't you be their lover then? Assuming that they prescribe to the same rule (a given, considering that the Spice Girls have a hive mind and would all follow this rule). The Spice Girls also have no friends beside each other. This leads to an endless cycle of not-quite-[bleep]ing, and you will never, ever get laid. Not that that's a new thing.[/hide]

 

Schrödinger's Cat

 

[hide=]A cat, along with a flask containing a poison, is placed in a sealed box shielded against environmentally induced quantum decoherence. If an internal Geiger counter detects radiation then the flask is shattered, releasing the poison which kills the cat. Quantum mechanics suggests that after a while the cat is simultaneously alive and dead. Yet, when we look in the box, we see the cat either alive or dead, not a mixture of alive and dead.[/hide]

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consider the door thing like this

 

 

 

I have a 3 sided(magic) coin and ask you to predict which one of the sides will show up, lets call them a, b, and c

 

 

 

you choose side a, I then alter the coin so that only sides a and b are left

 

 

 

initially you had a 1/3 chance of being correct, after I remove a side you have a 1/2 chance regardless of which of the remaining sides you choose.

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Orthodoxy is unconciousness

the only ones who should kill are those who are prepared to be killed.

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[hide=]As a point of general interest you can't divide by zero. Any number divided by zero does NOT = zero. A calculator will normally give: error, divide by zero error, or undefined (the latter being to generaly excepted answer). Zero is nothing, and you can't divide anything by nothing, you can't even divide nothign by nothing. It dosen't equal infinity, it is simply undefined. And thats from a mathmatical system that solved how to square root a negative (or any even root).

 

 

 

I like the one about half distances, and because an object must always travel half the distance to it's destination, it will never get there because everytime it gets half way, there is a new halfway. Unfortunatly thats more bad logic and lack of calulus (which actualy can be used to divide by zero, its called finding tanget lines) than anything else, and it is quite obviusly false.

 

 

 

There is also one about at any single point in time, nothing can move, since all movement is essentialy a distance for a given time interval (or a derivitive of that function such as acceleration, jerk and snap). If the given time interval is zero, then there can't be movement becuase we are back at tehhe whole dividing by zero thing. Acording to teh original idea, movement is immpossible becuase time is an infinate series of instantaneous points and there can be no movement at an instantaneous point in time.

 

 

 

Other than bad logic, infinity offers a few good one. First off, due to the nature of the concept of infinity, all infinitys are equal. There are also infinate numbers. Now consider this:

 

- The number of even numbers = infinity and the number of odd numbers = infinity so the number of even numbers = the number of odd numbers. Strait forward so far?

 

- There are an infinate number of numbers, so the # of even numbers = # of odd numbers = infinty = number of numbers

 

- There are an infinate number of numbers so there are also in infinate ammount of prime numbers therfore the # of numbers = the # of prime numbers. Now think about that one. To our minds, we know that there are definatly more numbers that there are prime numbers, especialy considering that numbers incluses prime (plus a whole lot more). Still, becuase of how all infinitys are equal, the statement stands.

 

 

 

Not really a paradox, but I realy like the mobius strip (just wikipedia it if you don't know what it is or how to make one). Everytime I make one and trace a line on it, it just blows my mind all over again. How can a 1 sided object (minus the edges) exist in 3D space? Even if you count edges, which adds 2 sides, you only have 3 sides. 3 sides is good enough you say? How about you go find me a D3 (3 sided die).[/hide]

 

Gratz on 2k posts

 

 

 

Also @ cannibalism look at the youtube vid a little higher up

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Pureprayer, you're awesome.
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An infinite loop that always increases a number by (.9 + .9 X .(# of zeros as times looped)1), hence .9, .99, .999, .9999, .99999, .999999

 

 

 

It's a number that's increasing infinity, yet never reaches 1. It's easily explainable (it's increasing by an infinity small amount), but the idea of something infinity increasing without reaching infinity is weird.

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An infinite loop that always increases a number by (.9 + .9 X .(# of zeros as times looped)1), hence .9, .99, .999, .9999, .99999, .999999

 

 

 

It's a number that's increasing infinity, yet never reaches 1. It's easily explainable (it's increasing by an infinity small amount), but the idea of something infinity increasing without reaching infinity is weird.

 

I thought .999999~... = 1?

 

 

 

1/3 = .333~

 

 

 

2/3 = .666~

 

 

 

1/3 + 2/3 = 3/3

 

 

 

BUT .333~ + .666~ = .999~

 

--------------------------------------------

 

Also 1/9 = .111~

 

 

 

1/9 * 9 = 9/9

 

 

 

.111~ * 9 = .999~

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You pick the car. You keep it.

 

You pick the car. You switch, and get the goat.

 

You pick Goat 1. You keep it.

 

You pick Goat 1. You switch and get the car.

 

You pick Goat 2. You keep it.

 

You pick Goat 2. You switch and get the car.

 

 

 

that is 50/50 odds

 

 

 

3 goats 3 cars as the final outcome

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Orthodoxy is unconciousness

the only ones who should kill are those who are prepared to be killed.

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