Question for Big Number Math Guys

[georged]

OK...

The chance of a tossed quarter landing on its edge (on a dead flat, clean, etc. surface) is one in 6000.

Here's my question:

How many tosses would it take for a TRILLION coins tossed simultaneously to ALL land on their edge...

...and for THAT to happen a trillion times in a row.

Imma gonna guess the answer is way north of the number of atoms in the Universe, or similar---some number that will make a googol look trivial---but I have no clue how to handle exponential calculations that size.

Why does it matter? My grrrlcat Lily wants to know, and she'll kick my ass if I disappoint her.

 

[Scottmi]

the answer is '42'

 

[brian64]

OK...

The chance of a tossed quarter landing on its edge (on a dead flat, clean, etc. surface) is one in 6000.

Here's my question:

How many tosses would it take for a TRILLION coins tossed simultaneously to ALL land on their edge...

...and for THAT to happen a trillion times in a row.

Imma gonna guess the answer is way north of the number of atoms in the Universe, or similar---some number that will make a googol look trivial---but I have no clue how to handle exponential calculations that size.

Why does it matter? My grrrlcat Lily wants to know, and she'll kick my ass if I disappoint her.


View attachment 235320
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I'm sorry, I don't know the answer.

But this is an interesting article I just thought I'd pass along...no particular reason...

How a Cat Parasite Controls Other Animals' Brains

Toxoplasma has the power to modify its host's brain and behavior, but to what extent this manipulation occurs in humans is still unclear...

How a Cat Parasite Controls Other Animals' Brains

Toxoplasma gondii, an insidious and common parasite spread by cats, controls its rodent host's brain—and may be manipulating our own behavior as well

www.scientificamerican.com

 

[mortonbriar]

I guess you need a trillion tossers. I only know 8 or 9 billion tossers...

 

[Brendan]

I guess you need a trillion tossers. I only know 8 or 9 billion tossers...

So we use both hands and double our chances?

 

[Zero]

My cat just sings opera all day. La la la la, la la la la, la la la la la la, la la la la! He's drivin' me nuts.

 

[RustiePyles CPG]

Well the article is based on a US Nickel, you asked about a quarter... Just doing some basic math a US quarter is about 24.26x1.75mm vs the nickles 21.21x1.95mm meaning that a quarter is 12.58% larger in diameter and 10.26% tinner,and the quarter has a reeded edge as opposed to the nickles plain mostly square edge all these things mean the quarter is exponentially harder to stand on edge to an order of magnitude that my peabrain is unable to calculate.
My best guess is that a quarter is 5055.6 times LESS likely to land on its edge meaning a quarter will land on it's edge 1 in 11,055.6 tosses.

While i do not possess the skills to determine the probability of 1 trillion tosses landing on edge 1 trillion times I can tell you it's so remote that you have a greater probability of being attacked by a shark in lake Superior while winning the Power Ball and simultaneously being struck by lightning. Which is roughly 1 in 4,048,000,000,306,000

 

[JOHN72]

I'm dizzy with all this coin tossing. Can't you make a better apple pie, or plant onions in the garden? That's how World War II started, boy.

 

[jguss]

So we use both hands and double our chances?

I think for our UK friends a tosser using both hands might convey a different image.

 

[RustiePyles CPG]

Rethinking your inquiry I've determined this to be a case of which is heavier a 1lb rock or a 1lb of feathers type of question. 1lb is 1lb, 1 in 6000 is 1 in 6000, there are zero chances it will happen two consecutive times let alone 1 trillion consecutive times. The answer is 0. You can tack on as many zeros as want after that and throw a 1 in there after a few dozen meaning however remote the possibility is there is a always a possibility. But the nearest whole number answer would be a resounding 0.

 

[Jbrewer2002]

Here is chat GPT’s answer when I copied your question and pasted in.


The probability of a single quarter landing on its edge is indeed one in 6000, which can be expressed as 1/6000 or approximately 0.0001667. However, when tossing multiple coins simultaneously, the probabilities are combined differently.
When you toss two coins, each with a probability of 1/6000 of landing on its edge, the probability that both coins will land on their edges simultaneously is (1/6000) * (1/6000).
Similarly, when tossing three coins, the probability that all three will land on their edges simultaneously is (1/6000) * (1/6000) * (1/6000).
In general, for 'n' coins tossed simultaneously, the probability that all 'n' coins will land on their edges is (1/6000)^n.
Now, you want to find the number of tosses 'n' such that the probability of all 'n' coins landing on their edges is equal to 1 in a trillion, which can be expressed as 1/1,000,000,000,000 or 0.000000000001.
Setting up the equation:
(1/6000)^n = 0.000000000001
To solve for 'n', take the logarithm of both sides:
n * log(1/6000) = log(0.000000000001)
Now, solve for 'n':
n = log(0.000000000001) / log(1/6000)
Using a calculator:
n ≈ 62,775,109,935
So, it would take approximately 62,775,109,935 tosses for a trillion coins tossed simultaneously to all land on their edge with a probability of one in a trillion

 

[kcghost]

I would have thought a simple 1/6000 * 1/1,000,000,000,000^2 would have been sufficient number of times to perform this calculation.

 

[Sobrbiker]

I think for our UK friends a tosser using both hands might convey a different image.

I’m red white and blue through and through and nearly retrohaled my coffee at the “tosser” comment!

 

[Jbrewer2002]

This was what I asked GPT. I didn’t even ask about a trillion in a row lol.
“
The chance of a tossed quarter landing on its edge (on a dead flat, clean, etc. surface) is one in 6000.

Here's my question:

How many tosses would it take for a TRILLION coins tossed simultaneously to ALL land on their edge..”

 

[brian64]

For a serious answer, I'd say the odds of it are about the same as a "big bang" somehow resulting in an intricately ordered universe with coded DNA producing highly complex life forms. In other words, just ain't gonna happen no matter how much time you give it.

 

[mso489]

I disbelieve the one in six thousand figure. I think the force of a falling quarter would tip it one way or the other in a greater number of cases than one in six thousand.

I don't intend to do the experiment, but I think physics are against those odds.

However, if the question is simply "what if it were one in six thousand," as a math exercise, then okay.

 

[georged]

I'm sorry, I don't know the answer.

But this is an interesting article I just thought I'd pass along...no particular reason...

How a Cat Parasite Controls Other Animals' Brains

Toxoplasma has the power to modify its host's brain and behavior, but to what extent this manipulation occurs in humans is still unclear...

How a Cat Parasite Controls Other Animals' Brains

Toxoplasma gondii, an insidious and common parasite spread by cats, controls its rodent host's brain—and may be manipulating our own behavior as well

www.scientificamerican.com

that is simply not true ... it is a myth ... humans cannot be controlled by cats ... lily is kind generous helpful and loving ... and i love her and want to pet her and feed her and make her happy in every way ... because lily is kind generous helpful and loving ... and humans are better off with cats in the world than no cats ... so much that all I want to do is make their lives better ... nothing else matters to me or should matter to any other human because cats are only kind generous helpful and loving ... they are so wonderful that mind control is not needed even if it was possible ... because it is not ... it is a myth ... humans cannot be controlled by cats and lily is kind generous helpful and loving ... and i must stop typing now to feed her the caviar i sold my truck to be able to buy for her

 

[olkofri]

that is simply not true ... it is a myth ... humans cannot be controlled by cats ... lily is kind generous helpful and loving ... and i love her and want to pet her and feed her and make her happy in every way ... because lily is kind generous helpful and loving ... and humans are better off with cats in the world than no cats ... so much that all I want to do is make their lives better ... nothing else matters to me or should matter to any other human because cats are only kind generous helpful and loving ... they are so wonderful that mind control is not needed even if it was possible ... because it is not ... it is a myth ... humans cannot be controlled by cats and lily is kind generous helpful and loving ... and i must stop typing now to feed her the caviar i sold my truck to be able to buy for her

Proof right there!

The smaller typeface and fragmentary writing—your cat made you type all that. She's countering "misinformation".

Now I know why all archvillians, from Blofeld to Dr Claw have cats.

 

[georged]

Rethinking your inquiry I've determined this to be a case of which is heavier a 1lb rock or a 1lb of feathers type of question. 1lb is 1lb, 1 in 6000 is 1 in 6000, there are zero chances it will happen two consecutive times let alone 1 trillion consecutive times.

I'm pretty sure the chances of two edge-flips in a row is simply one over 6000 squared... i.e. one in 36 million.

Which is what got me wondering about this. If it can be calculated THAT much, it must be "infinitely calculable". Rudimentary math, just taken to an absurd level.

Anyway, I just now emailed my kid to see what he says (he's a quantum physicist and actually does does crazy big number stuff for a living), so an answer might be forthcoming.

There's an equal chance he'll just say, "Dad. Seriously? You need to get out more", of course...

I'll let you know either way.

 

[Zero]

Laaaaaaaaaaaaaaaaaaaa...(2min. 1.08sec)