Suppose that asteroid impacts on the earth are modelled with a Poisson distribution. Asteroids of diameter 4m are estimated to enter the Earth's atmosphere once per year. Asteroids of diameter 1km are estimated to impact the Earth once every 500,000 years.
(a) What is the probability of exactly 2 asteroids of 4m diameter entering the atmosphere in a 6 month period?
(b) How many years are required for the probability of at least one 1km diameter impact to exceed 1%?
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