Math Problem
kill me
In the video game Minecraft, for each loaded chunk, every tick there is a $\frac{1}{100000}$ chance of a lightning strike during a thunderstorm. Assume a thunderstorm is currently active. (Given: $1$ second $= 20$ ticks)
(a) Find the expected value of lightning striking in $1$ chuck in an hour.
(b) Using the value in (a), or otherwise, find the probability there are at least $1$ lightning strike in $1$ loaded chuck in an hour. Correct your answer to $5$ decemial places.
(c) The weather is considered severe when $10$ or more chucks have at least $1$ lightning strike over an hour.
(i) Find the probability that the weather is severe when $12$ chunks are loaded.
(ii) Given that the weather is severe, find the probability that there are at least $12$ lightning strikes in total across $12$ chunks during the $1$ hour.
(d) In one chunk, how long does it take for the first lightning strike to occur where the probability is higher than $0.4$? Express your answer in minutes.