I hope someone can give me some pointers for what might be a fairly trivial problem.
We have an experimental test where measurements are made on a regular grid or checkerboard - say a 7 by 7 square. For simplicity the measurement at each point can be reduced to a random variable from a binomial distribution where the probability of a failure (F) is assumed to be quite small (say 10%). This generates a checker board of results where each square in the grid is either F or P (pass). Also (at least for the time being) I want to assume that each measurement is independent (no spatial correlations for example). My question is this: what would be the probability of getting say 3 Fs that are contiguous, or adjacent on this sort of grid? Or indeed, what is the probability of getting n number of contiguous Fs in a grid of N by N size - or even on an irregular grid?
Many thanks in advance for your help with this.
Dr. David Crabb
Department of Optometry and Visual Science,
City University,
Northampton Square, London EC1V 0HB.
Tel: 0207 040 0191 [log in to unmask]
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