probability word problem

Question

If I travel 523 km across 77 hours and lighting randomly strikes a 3 m2 area every second within a 1307 km2 region, what is the probability that I am struck by lighting at some point during my journey?

Answer 1

Assuming the 523 km is traveled on a random path inside the 1307 km2 region, and coverting the 1307 km2 region into meters becomes 1,307,000,000 m2

The probability of getting hit in exactly one second is then 3/1,307,000,000

using compliments, the probability of not getting hit become (1-(3/1,307,000,000))ⁿ

Therefore getting hit at least once would be the compliment of that becoming 1-(1-(3/1,307,000,000))ⁿ

n is for time in seconds because the problem stated it strikes every second, and its over 77 hour time frame, there is 277,200 seconds in 77 hours.

Plug that in for n and punch it into a calculator and you get 6.36x10^-4

That is the same thing as 0.00636 which means you have a 0.063% chance.