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A factory has 2 firms producing the same type of product. The numbers of errors per product produced by firm A and firm B follow

A factory has 2 firms producing the same type of product. The numbers of errors per product
produced by firm A and firm B follow Poisson distributions with means of 0.1 and 0.2 respectively.
Furthermore, errors occur independently between products regardless the producing firms.
(a) Suppose that the proportion of products produced by firm A is 0.25. In a random sample of 15
products produced by this factory, find the probability that there are more than 12 products
that have exactly 3 errors.
(b) In a random sample of 100 products produced by firm A, find the probability that there are
from 60 to 95 products that have at least 1 error.
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