(a) A manufacturer produces light bulbs which are tested in the following
way: A batch is accepted in either of the following cases:

(i) The first sample of 5 bulbs contains no faulty bulbs;

(ii) The first sample of 5 bulbs contains at least one faulty bulb but a
second sample of 5 bulbs contains no faulty bulb. If 10% of the
bulbs are faulty, what is the probability that the batch is accepted?

(b) A bag contains 15 identical marbles of which 3 are back. Keshi picks a
marble at random from the bag and replaces it. If this is repeated 10
times, what is the probability that he

(i) did **not **pick a black ball?

(ii) picked a black ball **at most **three times?