Talk: Living Hoe

Showing my work

This is for xbony2 ❣️:

Let $P({\text{Regen}})={\frac {1}{80}}$ for the chance a point of durability will be restored in a tick.

Therefore, $P({\text{not Regen}})=1-P({\text{Regen}})=1-{\frac {1}{80}}={\frac {79}{80}}$

For a second there are 20 ticks, each of which are independent events. We are going to be focusing on 1 second, or $n=20$. For all the calculations determining whether a point is regenerated in those 20 ticks, there will be twenty ${\frac {x}{80}}$. To calculate the probability of the outcomes of events happening, we'd have to do Event A AND Event B AND Event C... or mathematically:

${\text{Event A}}\times {\text{Event B}}\times {\text{Event C}}\times \cdot \cdot \cdot$

If we are looking for the probability that $P({\text{Regen}})$ happens exactly once in a second (and all the other times $P({\text{Regen}})$ doesn't happen exactly once):

$P({\text{Regen}})^{1}\times P({\text{not Regen}})^{19}={\frac {1}{80}}\times ({\frac {79}{80}})^{19}=0.00984$

In other words, the probability that a point is regenerated exactly once in a second (and all other times it doesn't happen, including the times where it happens more than once) is a little under 1%.

If we are looking for the probability that $P({\text{Regen}})$ happens at any point in one second (and multiple times are allowed), it would be the complement of a second where no point is regenerated. So we first take the probability that all 20 ticks will not regenerate a durability point, or $({\frac {79}{80}})^{20}=0.77757$; there is a 77.76% chance that no durability will be restored in a second. The events where that doesn't happen would be if any of the ticks regenerate a durability point; this can happen once, twice, thrice, as many times so long as at least one tick regenerates a point. This would be mathematically expressed as

$P({\text{Regen at least once}})=1-({\frac {79}{80}})^{20}=1-0.77757=0.22242$

In other words, the probability that regeneration occurs in any given second (and can happen more than once) is roughly 22.25%. --SirMoogle (talk) 22:29, 9 October 2017 (UTC)

okay -Xbony2 (talk) 23:57, 9 October 2017 (UTC)

SirMoogle Did I get the probability right on Tree Fluid Extractor? -Xbony2 (talk) 01:01, 10 October 2017 (UTC)

xbony2 You sure did. 👍 --SirMoogle (talk) 20:40, 10 October 2017 (UTC)