Talk:Living Hoe

Showing my work
This is for ❣️:

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)
 * Did I get the probability right on Tree Fluid Extractor? 𝜘 -Xbony2 (talk) 01:01, 10 October 2017 (UTC)
 * You sure did. 👍 --SirMoogle (talk) 20:40, 10 October 2017 (UTC)