On a particular production line the probability that an item is faulty is 0.08. In a quality

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On a particular production line the probability that an item is faulty is 0.08. In a quality control test, items are selected at random from the production line. It is assumed that quality of an item is independent of that of other items.

(a) Find the probability that the first faulty item (i) does not occur in the first six selected, (ii) occurs in fewer than five selections.

(b) There is to be at least a 90% chance of picking a faulty item on or before the nth attempt. What is the smallest number n?

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