Question 697294: A diamond can be classified as either gem-quality or industrial-grade. 92% of diamonds are classified as industrial grade.
1. What is the probability that 2 randomly selected diamonds are industrial-grade.
2. Waht is the probability that 9 randomly selected diamonds are industrial-grade.
3. What is the probability that at least 1 of 9 randomly selected diamonds is gem-quality? Would it be unusual that at least 1 of 9 randomly selected diamonds is gem -quality.
Answer by Positive_EV(69)   (Show Source):
You can put this solution on YOUR website! Assuming that all gems are selected independently of one another:
1) The probability of two diamonds being industrial grade is equal to the probability of the first diamond being industrial grade times the probability that the second diamond is industrial grade. This is equal to
 , or 84.64%.
2) This is similar to problem 1, except there are now 9 diamonds. The probability they are all industrial grade is the probability of the first diamond being industrial grade times the probability that the second diamond is industrial grade times the probability the third diamond is industrial grade times ... times the probability the ninth diamond is industrial grade. This is equal to
 , or 47.22%.
3) The event that at least one diamond is gem quality is the compliment of the event that all of the gems are industrial grade; that is, either all of the gems are industrial grade, and if not, at least one is gem quality. The probability of a complementary event happening is
1 - the probability of the original event happening.
So the probability of getting at least one gem quality diamond of nine is
1 - the probability that they are all industrial grade, which from part 2 is
1 - .4722 = .5278, or 52.78%. So, not only is it not unusual for a gem quality diamond to appear given nine gems, it's more likely than not.
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