3 Robert maintains a server farm with 20 identical computers

3. Robert maintains a server farm with 20 identical computers. For convenience, these computers are labeled C,, Cn. A are labeled C1, C2,... . Cn. A software virus has infected exactly 3 machines, and every computer is equally likely to be affected by the virus.

Solution

a)

There are 20C3 ways to choose 3 infected computers.

Now, if we fix C1 as infected, there are 19C2 ways to choose the other two.

Thus,

P(C1 is infected) = (19C2)/(20C3) = 0.15 [ANSWER]

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b)

There are 20C3 ways to choose 3 infected computers.

Now, if we fix C1 and C2 as infected, there are 18 ways to choose the other one.

Thus,

P(C1 and C2 are infected) = (18)/(20C3) = 0.015789474 [ANSWER]

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C)

Note that

P(C1 or C2) = 1 - P(C1 nor C2 are affected)

There are 18C3 ways so that C1 and C2 are not affected.

Thus,

P(C1 or C2) = 1 - (18C3)/(20C3) = 0.284210526 [ANSWER]