[2] Suppose the migration of butterflies from southern Canada to a south Florida

Question

[2] Suppose the migration of butterflies from southern Canada to a south Florida butterfly sanctuary is a Poisson process with an average rate of 10 per week. That is, the probability that n number of butterflies will arrive in time t is given by () = ^((-t)(t)^n)/n! , where is the rate with which they arrive. Suppose also that 1/5 of these butterflies are of a particular species. What is the probability that no butterflies of this species will arrive at the sanctuary during the month of January?

Explanation / Answer

Probability that no butterflies of this species will arrive at the sanctuary during the month of January

= (1/5) * (0) = (1/5) * e^((-t)(t)^0)/0! = e^((-t)

= 10 (Given)

t = 31 days ( January month)

31 days = 31/7 weeks

Required probability = (1/5) * P(0) =(1/5)* e^((-t) = e^(- 1* 10 * (31/7)) = (1/5) * e^( - 44.285) = 0

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