If a piece of computer equipment will fail once a year and be unavailable for 1.5 hours, how do I calculate the probability of the failure occurring each hour of every day
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If your question is:
We will count the failure event itself, which happend once per year, giving:
0.01142% chance of experiencing a failure in a given hour.
If the question was:
(as is implied by the duration given), then:
The probability of the single failure overlapping with a given hour is:
Number of days in a year = 365d/y
0.01712% probability of having some unavailability within a given hour.