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$($Computer project$)$ Twenty computers are connected in a network. One computer becomes infected with a virus. Every day, this virus spreads from any infected computer to any uninfected computer with probability $0\mathrm{.}1.$ 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. These are some advice on how to solve this: $1.$ Decide on N $=($large number$)$ of simulations Loop the simulation N times, collect data, then average. $2.$ A single simulation is also a while$-$loop there can unknown # of days: from day $1$ when the virus is introduced until the day when the network is clean. $3.$ Network: C$1,$ C$2,$ C$3.......................,$ all conected to each other. $4.$ In the beginning of a simulation, i$.$e$.,$ before day $1$ infect one computer, say C$1($ or a random one$)5.$ In a single day: a$)$Morning Virus spreads Currently infected: $...........$ Currently clean: $.............$ For each "infected$/$clean in the morning" pair $($connection$)$ its a Bernoulli trial with p $=0\mathrm{.}1$ for the virus to spread along this connection. b$)$Afternoon: The technician shows up and tries to clean. If currently infected is less than or equal to $5$: all get cleaned, finish the simulation. If currently infected more than $5$: randomly chose $5$ of them to clean. $6.$ what do we need to count in a single simulation? a$)$ Number of days c$)$ For each computer, a flag indicating if it has been infected$($has had the virus on it$)$ at least once during the simulation, In the end: # of computers for which this flag is true. b$)$ Event: # of computers infected$($from part $($c$))=20$ give code.