MATH 350 Quiz 06

1. Consider a large-scale electrical grid that distributes power to a city. On average, $2$ substations experience a failure in a month due to various issues like equipment malfunction, weather-related incidents, or other external factors.
   1. What type of distribution is appropriate to model the number of substation failures per month?
   2. What is the probability that in a given month, exactly 3 substations experience a failure?
   3. What is the probability that in a given month, no substations experience a failure?
   4. If an engineering team can only handle fixing 1 substation failure a month, what is the probability that they will be overwhelmed with the number of failures in a given month? And should you hire another team?
   5. Write the probability from above another way. If you used an infinite sum above, use a trick plus a finite sum here. On the other hand, if you used a finite sum above, write out the probability as an infinite sum here.
   6. Over a 3 month period, what is the probability that exactly 6 substations experience a failure?