According to the National Center for Health Statistics, the life expectancy for a 50-year-old American female is 32.5 years. Assuming that, from age 50, the survival of American females follows an exponential distribution, determine the following probabilities.

(a) The probability that a randomly selected 50-year-old American female will live beyond 90 years of age (at least 40 more years)
(b) The probability that a randomly selected 50-year-old American female will live between 30 and 50 more years