I came across a problem for which I found two answers and I don't know which is the correct one.
At a particular site, the probability of occurrence of moderate earthquake in a single minute is assumed to be $10^{-8}$. If the events in succeeding minutes are statistically independent, what is the probability that there will be no moderate earthquake during the 50 year life of the building.
Probability of occurrence of moderate earthquake in a minute $=10^{-8}$
Answer 1:
Probability of occurrence of moderate earthquake in 50 years
$=10^{-8}\times60\times24\times365\times50=0.2628$
(Ignoring leap years)
Probability that there will be no moderate earthquake in 50 years,
$=1-0.2628=0.7372$
Answer 2:
Probability that there will be no moderate earthquake in a minute
$=1-10^{-8}$
Probability that there will be no moderate earthquake in 50 years,
$=(1-10^{-8})^{60\times24\times365\times50}=0.7689$
Both answers are pretty close, but which is the correct answer?