Ten participants are randomly selected from a population of patients with history of heart disease to be tracked in a health study. The study begins with an initial assessment of health status. The participants are instructed to return for a follow up visit one year after the initial assessment.
For these ten participants, the time (in years) from the initial assessment to the first heart attack has an exponential distribution with mean 5.
The times to first heart attack for these participants are independent.
What is the probability that prior to the one-year follow up visit, three or more of the participants have experienced their first heart attack since initial assessment?
The time (in years) to failure of an electronic device follows an exponential distribution with mean 10. Twelve such devices are randomly selected for a quality control study.
The times to failure for these devices are independent.
What is the probability that at least 9 of the devices will still be working after 5 years?
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