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Math

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A large company has a private computer network connecting 300 different sites. Each site is connected to the network independently with a switch that fails with probability 1% on any given day.

1. What is the probability that exactly two of 300 sites lose their network connection on any given day?

2. The company is considering buying better switches. What failure rate p would the switches need to have in order for there to be 99% probability that none of the 300 switches fail on
a given day? Give your answer to 5 decimal places.

3. The company is considering replicating their core software system across the network such that the system is operable so long as fewer than k switches fail. If switches fail with
probability 1% on any given day, what is the smallest k that ensures that the core system is up 99% of days.

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