Problem
A patient has been diagnosed with a serious disease. The lifetime of patients with this disease are approximately exponential with expected value of 10 years, after initial diagnosis.
1. What is the probability that a patient who is diagnosed today with still be alive 15 years from now?
2. Given that a patient is still alive after 5 years, what is the probability the patient will still be alive 15 years after initial diagnosis?
3. 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?