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Twenty computers are connected in a network. one computer becomes infected with a virus. this virus spreads from an infected computer to any uninfected computer with probability 0.1.

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Twenty computers are connected in a network. One computer becomes infected with a virus. Every day, this virus spreads from an infected computer to any uninfected computer with probability 0.1. Also, every day, a computer technician takes 5 infected computers at random (or all infected computers, if their number is less than 5) and removes the virus from them. Estimate:

(a) the expected time it takes to remove the virus from the whole network;

(b) the probability that each computer gets infected at least once;

(c) the expected number of computers that get infected.

 

Instructions

*** At a very basic level, which is good enough for our purposes for now, the Monte Carlo method amounts to repeated simulations of the phenomenon under study. (Of course, there's a lot more to the story, as always; but we've got to start with the basics.) So the main part is to implement a simulation of what's described in the problem. Make sure that your simulation involves randomness exactly as described! And then you run it repeatedly in a loop.

*** First make sure that your Monte Calro simulation works with the provided values. But then, to make your project a bit more advanced, provide an option to choose input values, such as the number of computers, the probability of spreading the infection, and the number of computers repaired.

***To get decent results, make the number of runs large enough. You can hard-code it for now, as some large number, like N = 10000 or something.

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