2 John is observing butterflies being blown across a fence in a strong wind. He uses the Poisson distribution with mean 2.1 to model the number of butterflies he observes in one minute.

1. Find the probability that John observes
   (A) no butterflies in a minute,
   (B) at least 2 butterflies in a minute,
   (C) between 5 and 10 butterflies inclusive in a period of 5 minutes.
2. Use a suitable approximating distribution to find the probability that John observes at least 130 butterflies in a period of 1 hour. In fact some of the butterflies John observes being blown across the fence are being blown in pairs.
3. Explain why this invalidates one of the assumptions required for a Poisson distribution to be a suitable model. John decides to revise his model for the number of butterflies he observes in one minute. In this new model, the number of pairs of butterflies is modelled by the Poisson distribution with mean 0.2 , and the number of single butterflies is modelled by an independent Poisson distribution with mean 1.7.
4. Find the probability that John observes no more than 3 butterflies altogether in a period of one minute.