Compare a binomial majority with waiting for one further red pen

A manufacturer produces pens in two colors, red and blue. On average, 35% of the pens produced are red pens.

(i) Find the probability that in a sample of 10 pens, more than half of them are red pens.2 marks

(ii) The manufacturer offers a special price on red pens by selling them in packs of six. Pens are selected at random to fill each pack. Given that five red pens have been selected, find the least value of $n$ such that the probability that at most $n$ more pens need to be selected to complete a pack of 6 red pens is greater than 0.98.4 marks