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6) To construct sample spaces for experiment in which we deal with categorical data, we often code the various alternatives by assigning them numbers....
5.6) To construct sample spaces for experiment in which we deal with categorical data, we often code the various alternatives by assigning them numbers. For instance, if persons are asked whether their favorite color is red, yellow, blue, green, brown, white, purple, or some other color, we might assign these alternatives the codes 1, 2, 3, 4, 5, 6, 7, and 8, respectively. If A= {3, 4}, B= {1,2,3,4,5,6,7}, and C= {5, 6, 7,8}, list the outcomes that comprise each of the following events:
(a) B'; (c) A ∩ B; (e) A' U C;
(b) A U B; (d) C'; (f) B ∩ C'.
5.20) In a study of the adequacy of fuel supplies, C stands for the event that a power plant Will use coal and E is the event that it will be able to provide enough electricity. States in words the probabilities expressed by
(a) P (C'); (d) P (C ∩ E);
(b) P (E'); (e) P (C' ∩ E);
(c) P (C U E); (f) P (C' ∩ E');
5.54) Given P(A) = 0.59, P(B) = 0.46, and P( A ∩ B) = 0.28, draw a Venn diagram, fill in the probabilities associated with the various regions, and thus determine
(a) P ( A' ∩ B); (c) P ( A U B);
(b) P (A ∩ B'); (d) P ( A' ∩ B').
5.68) According to the mortality tables of a life insurance company, the probability that policyholder Alpha will be alive 10 years from now is 0.50, and the probability that policyholder Beta will be alive 10 years from now is 0.60. What is the probability that both policyholder, Alpha and Beta, will be alive 10 years from now? Assume that these are independent events. (If both policyholders worked together in a very hazardous occupation, their mortalities might not be independent.)
