A carbon monoxide detector in the Wheelock household activates once every 200 days on average. Assume this activation follows the exponential distribution. What is the probability that:
a. There will be an alarm within the next 60 days?
b. At least 400 days will pass before the next alarm?
c. It will be between 150 and 250 days until the next warning?
d. Find the median time until the next activation.