Homework: UNIT 3 - Section 5.3 Homework Score: 0 of 1 pt X)5.3.18 4 of 6 (6 comp
ID: 3065301 • Letter: H
Question
Homework: UNIT 3 - Section 5.3 Homework Score: 0 of 1 pt X)5.3.18 4 of 6 (6 complete) HW Score: 52.78% Ques A diamond can be classified as either gem-quality or industrial-grade. Suppose that 88% 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.)Explanation / Answer
a) P(both are industrial grade) = (0.88)^2 = 0.7744
b) P(all eight are industrial grade) = (0.88)^8 = 0.3596
c) P(at least one of the eight randomly selected diamonds is gem quality) = 1 - P(no one of the of the eight randomly selected diamonds is gem quality) = 1 - (0.88)^8 = 1 - o.3596 = 0.6404
As the probability is greater than 0.05(0.6404 > 0.05), so it is not unusual.
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