A cloud company has 20 computers total. Out of the 20 computers, 9 run web serve

Question

A cloud company has 20 computers total. Out of the 20 computers, 9 run web servers and 12 host databases. Furthermore, 8 machines offer file sharing. Note that a particular machine can offer multiple services. In fact, 2 computers provide web services, databases and file sharing concurrently.

(a) 1 If a computer is selected at random, what is the probability that it hosts a database?

(b) An audit reveals that, out of 12 machines that host databases, one fourth of them also offer file sharing. How many machines that host databases do not provide file sharing?

(c) Suppose that a web server is selected at random. The probability that this computer provide file sharing is 1/3. If a file sharing machine is chosen randomly, what is the probability that it is also a web server?

(d) Out of the computers that run databases, 5 are also offer web services. If a database server is selected at random, what is the probability that it does not offer any other services?

Explanation / Answer

1)  Probability that it hosts a database= 12/20 = 0.6 Answer

2) Machines that host databases do not provide file sharing = 12- 12/4= 9 Answer

3) No. of computers that provide web service as well as file sharin = 9* 1/3 =3

Therefore, if a file sharing machine is chosen randomly, the probability that it is also a web server :

=3/8 =0.375 Answer

4) Desired probability = 7/12 Answer

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