A job arriving in a certain cloud computing system must be routed to one of eigh

Question

A job arriving in a certain cloud computing system must be routed to one of eight servers. Due to the loads, the servers all have different rates. Routing the job to the server with the highest rate would require sampling the rates of all eight servers. Instead, the rates of three randomly selected distinct servers are sampled (all choices being equally likely) and the job is routed to the sampled server with the highest service rate.

Let CC be the event the job is assigned to one of the two servers with the highest rates. What is P(C)? Present your answer in an irreducible fraction.

Explanation / Answer

P(C) = Probability that at least one of the two server with highest rate is selected in the sample of 3 = 1 - P(none of the two server with highest rate is selcted)

= 1 - 6C3/8C3

= 1 - 5/14

= 9/14

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