Question

a diamond can be classified as either gem quality or industrial grade. suppose that 87% of diamonds are classified as industrial grade

A diamond can be classified as either gem-quality or industrial-grade. Suppose that 87% 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 aleight 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 to (Round to four decimal places as needed.) (b) Eight diamonds are chosen at random. What is the probability that all eight diamonds are industrial-grado? The probability is I (Round to four decimal places as needed) (e) 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

Answer 1

Given P(industrail grade) = 0.87 and P(gem-qualtiy) = 0.13

a) P(both dimonds are industrial-grade) = 0.87*0.87 = 0.7569

b) P(eight diamonds are industrial-grade) = 0.87^8 = 0.3282

c) P(At least 1 diamonds is gem-quality) = P(X >= 1 )
= 1 - P(X <1)
= 1 - P(X = 0)
= 1 - P(none of gem-quality out of eight)
= 1 - 0.87^8
= 1 - 0.3282
= 0.6718

It would usual that at least one of eight randomly selected diamonds is gem-quality