PROBABILITY Diamonds Sample Point Sample Space and Probabil

PROBABILITY - Diamonds, Sample Point, Sample Space and Probabilities

ATTENTION: If any theorem, definition, lemma or formula is used in the answer, it should be stated and explained why it is been used. Even though the problem may look simple, this is a probability question. Solution needs to be shown STEP by STEP with MATHEMATICAL JUSTIFICATION. Solution wihtout detailed work won\'t be marked. Solution needs to show how and why. FORMAL ANSWER should be applied.

Three diamonds are to be graded from lowest to highest by an expert jeweller. That is one diamond will by identified as best, another as second best, and the remaining diamond as worst. (a) Describe one sample point for this experiment. (b) List the sample space. (c) Assume that the expert jeweller is in a rush and randomly assigns ranks to the three diamonds. One of the diamonds is of much better quality than the others. What is the probability that the expert jeweller ranks the best diamond no worse than the second best?

Solution

a) each sample point represents the quality of each diamond.

b) S={good, better, best} or we can rank the diamonds according to their quaity and write th sample space as S={1,2,3}

c) all the three diamonds have probability 1/3 of being assigned ranks.