Suppose that in manufacturing process, the probability of a certain item being defective

Suppose that in manufacturing process, the probability of a certain item being defective is p=0.05. Suppose that the quality of an item is independent of the quality of the other manufactured items. An inspector selects six items at random and let X equal the number of defective items in the sample space.

(i) How is X distributed?

(ii) Find the probability of at most two defective and at least two defectives.


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