Screws produced by a machine in a large company are packaged in packs of 50 screws each. The company believes that a pack cannot be

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Screws produced by a machine in a large company are packaged in packs of 50 screws each. The company believes that a pack cannot be sold if it contains at least three defective screws. If it is known that the probability of a screw being defective is 0.03,

(i) find the probability that a pack cannot be sold;

(ii) to decide whether a pack should be sold, an employee checks five screws at random and decides that a pack should not be sold if it contains at least one defective screw. Find the probability that a rejected pack contains less than three defective screws, so that it could have been sold.

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