A diamond can be classified as either gem-quality or industrial-grade 90% of dia

Question

A diamond can be classified as either gem-quality or industrial-grade 90% of diamonds are classified as industrial-grade. (a) Two diamonds are choosen at random. What is the probability that both diamonds are industrial-grade? (b) Eight diamonds are choosen 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) The probability is (Round to four decimal places as needed.) (b) The probability is (Round to four decimal places as needed.) (c) The probability is (Round to four decimal places as needed.)

Explanation / Answer

Ans: Probability of success i.e. of being industrial grade=0.9

a) Probability that both of them are industrial grade=0.92 =0.81

b)Probability that 8 of them are industrial grade=0.98 =0.4305

c)Probability of atleast 1 of gem quailty of 8 selected =1-P(none of them is gem quality)=1-P(all of them are of industrial grade)=1-0.98 =1-0.98 =1-0.4305=0.5695

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