A binomial model within a second binomial model

On average, 30% of the patients having a certain medical treatment experience severe headache. A random sample of 12 patients is given the treatment.

(i) Write down the distribution of the number of patients who experience severe headache, and state an assumption for the choice of the distribution.

(ii) Find the probability that fewer than 3 patients experience severe headache.

(iii) Five random samples of 12 patients are given the treatment. Find the probability that two of these five samples have fewer than 3 patients who experience severe headache.