Question

Mr. Fox is not the kind of person who rests. He and Batman get back to business. He is making some sort of system that gives info about the bad guys automatically.
He finds out that probability of Batman finding some criminal is 609/625 in 20 days.
But they don’t have that much time. Bane has set a deadline of 5 days to blow off the city.
What are the chances that Batman will catch Bane in 5 days and save Gotham city?

Answer 1

Let's assume that Batman's probability of finding some criminal is daily constant. Then the probability of Batman finding some criminal in a day is

609/625/20 = 609/12500.

Therefore, the probability of Batman finding Bane in a five day period is

5*609/12500 = 609/2500.