Question

3. Robert maintains a server farm with 15 identical computers. For convenience, these computers are labeled C1,C2,...,C15. A software virus has infected exactly 4 machines, and every computer is equally likely to be affected by the virus.
(a) What is the probability that computer C1 is infected?

(b) What is the probability that computers C1 and C2 are both infected?

(c) What is the probability that computer C1 or computer C2 (or both) is affected?'

(d) A job is submitted to the server farm, and it requires 5 computers. What is the probability that this job runs on 5 virus-free computers if it is randomly assigned to five machines in the farm?
(e) Suppose that a virus-free machine finishes before an infected machine with probability 2 3. Also, the probability that a virus-free machine finishes before another virus-free machine is equal to 0.5, and similarly, the probability that an infected machine finishes before another infected machine is equal to 0.5. Computer C1 and computer C2 are assigned tasks at the same time. What is the probability that C1 is one of the four infected machines given that C1 finishes after C2?

Answer 1

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