Answer all questions with explanation

1. Let T be the time-untildeath of a randomly selected newborn. It is assumed that T follows a uniform distribution between ages 0 and 100. Now consider Alyssa and Cristian, whose ages are 55 and 60, respectively. Assume that their timesuntildeath are independent random variables. (a) Calculate the probability that both Alyssa and Cristian survive at least 20 more years. [Hint: use the conditional probability rule for each person] (b) Calculate the probability that both Alyssa and Cristian die within the next 20 years. [Hint: use the conditional probability rule for each person]