Suppose your system has been developed and deployed and is operating in some environment. The environment has three possible (mutually exclusive) weather conditions: normal, rainy, and hot. The rainy and hot days pose a risk to the design (can cause a system failure), but normal days don’t pose a risk. Assume that all other risks for failure other than weather are extremely small and can be neglected. Based on historical information it’s expected that half of all days will have normal weather, one quarter of the days will be rainy, and one quarter will be excessively hot. The probability of a failure on normal days is 0%, for rainy days 0.2%, and for hot days 0.1%. Assuming that the type of weather the next day will have is selected at random, and that the effects of weather are statistically independent, what is the probability of not having a failure for 120 days in a row
