A diamond can be classified as either gem-quality or industrial-grade. Suppose that 85% of diamonds are classified as industrial-grade. (a) Two diamonds are chosen at random. What is the probability that both diamonds are industrial-grade? (b) Eight diamonds are chosen at random. What is the probability that all eight diamonds are industrial-grade? (c) What is the probability that at least one of eight randomly selected diamonds is gem-quality? Would it be unusual that at least one of eight randomly selected diamonds is gem-quality? (a) Two diamonds are chosen at random. What is the probability that both diamonds are industrial-grade? The probability is (Round to four decimal places as needed.) (b) Eight diamonds are chosen at random. What is the probability that all eight diamonds are industrial-grade? The probability is (Round to four decimal places as needed.) (c) What is the probability that at least one of eight randomly selected diamonds is gem-quality? The probability is: (Round to four decimal places as needed.) Would it be unusual that at least one of eight randomly selected diamonds is gem-quality? It would that at least one of eight randomly selected diamonds is gem-quality.

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