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.)