Some of the 270 spruces of a small forest stand are infested with rot (a fungus affecting first the core of the stems). Samples are taken from the stems of 30 randomly selected trees.

(1) If 24 trees from the 270 are infested, what is the probability that there are less than 4 infested trees in the sample?

Determine this probability both by the binomial approximation and by the Poisson approximation to the hypergeometric distribution.

(2) If the sample contains six infested trees, what is the most likely number of infested trees in the forest stand?