Well?

>>8284179
~0

~1

>>8284179
1

>>8284179
50/50
it either succeeds or not

>>8284179
~1

>>8284179
would be hard to calculate that with a calculator due to precision problems.

my best bet would be using the closed form for the exponential and then hope i get a geometric series somehow

>.9999999 != 1.0

Prove me wrong, losers

>>8285672
We can't.
[math]0.999... = 1[\math] though

>>8284179
Wait fuck it's definitely not 1.

If you have 9/10, you would have to raise it to 44 to get a value equal to less than 0.01. With 99/100, you would have to raise it to 459 to get a value equal to less than 0.01.

The equation to find the exponent needed to get a value of less than 0.01 for a fraction with n ones is [math]4.495e^{2.307n}[/math]. It's not exact, but it's close enough for us to work with.
Plugging in 1014 tells us that the fraction in parentheses must be raised to [math]3.95314... \times 10^1016[/math] to get a value of less than 0.01. Because the value in parentheses is only being raised to [math]10^155[/math], we can automatically rule out that the answer is 1.

If I wanted a decimal value whose tenth place was less than 9, starting with the decimal 0.9 (fraction: 9/10), I would have to raise it to 2 to achieve that. For 0.99 (99/100), I'd raise it to 11. The equation to find the exponent needed to raise a decimal with n 9s in it in order to get a tenths place of less than 9 is [math]0.148e^{2.246n}[/math]. Plugging 1014 into this yields [math]1.78494... \times 10^988[/math].
Thus, P(any state succeeds) = ~0.

>>8285846
[math]10^{1016}[/math], [math]10^{155}[/math], and [math]10^{988}[/math] respectively. Forgot how fucked exponents are in Latex.

>>8284179
There's no measurement system that would be accurate to a factor of 1000.

therefore, 1-10^-1014 is effectively 1
1^(10^155) is 1

therefore, 1 - 1 = 0

the exact answer is non zero, but close enough to zero that it doesn't matter.

Why are some of you saying it's one?
Just looking at it, it's real close to zero but not zero.

>>8284179
[math](1 - 10^{-1014})^{10^{155}} = 1 - 10^{155} \cdot 10^{-1014} + \ldots[/math]
so [math]\approx 10^{-859}[/math]