A thin sheet of gold foil (one atom thick) is fired upon by a beam of neutrons.

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A thin sheet of gold foil (one atom thick) is fired upon by a beam of neutrons. The neutrons are assumed equally likely to hit any part of the foil but only "see" the gold nuclei. Assume that for a beam containing many neutrons, the average number of hits is two.

(a) What is the probability that no hits occur?

(b) What is the probability that two hits occur?

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