A patient has been diagnosed with a serious disease. The lifetimes of patients with this disease are approximately Exponential with expected value 10 years, after their initial diagnosis.
a. What is the probability that a patient who is diagnosed today will still be alive 15 years from now?
b. Given that a patient is still alive after 5 years, what is the probability the patient will still be alive 15 years after the initial diagnosis?
c. If 5 people are diagnosed with this disease today, what is the probability that all 5 of them will be alive 15 years from now?