A beam of 1 ev neutrons with beam density 10^3 cm^-3 strikes a 1 micron thick pure gold target. If the beam cross section projection on the target is 1mm^2 and the total interaction cross section is 99 b, what is the interaction rate in the target? What are the probabilities of interaction and non-interaction? If the beam density were increased ten fold, what are the new reaction rate and probabilities?