How many hits will happen before a series of n misses?

Question

Mathematics

There is a range of numbers from 0 to 99.99. A series of numbers is selected from this interval. The program generates every iteration a random number from the first interval. How to calculate how many hits in the target row will pass (on average) until a series of n misses occurs?
The formula should take the chance of success (that is, if the target range is 0-20, then the chance of success is 20%) as a single integer and the number of misses itself.
Thank you all in advance)

Answer 1

You have 10000 values. You choose N values. So the probability of hitting is p0 = N/10000.
Well, the theory goes on. You need to find the probability of k hits in a row followed by n misses in a row. Hence p(k,n) = p0^k*(1-p0)^n. Then you set the confidence probability p1, they say, let the event occur if its probability is not less than 0.9. Well, choose such k and n so that p(k,n)>=p1.
And from this theory, using numerical methods, derive the formula you need in the program yourself.