If the probability of discovering a new planet within the next 1,000 years is 0.99, what is the probability that we will discover a new planet within the next 200 years?
Note: that each discovery of a planet is independent of each other.
I want to use the Poisson process formula, but I don't think that is correct since the probability is given out of 1000 trials, and we are solving for 200 trials.
Assuming you meant at least $1$ in $1000$ years, then you could use an exponential distribution for finding none, which is $0.01$ for $1000$ years. Therefore for $200$ years the probability for finding none is the fifth root, which is equal to $0.3981,$ so the probability of finding at least one in $200$ years is $0.6019.$