Answer to Question #308084 in Statistics and Probability for FAIZ

Question

A mainframe computer has 4 ports. At any given time each port is either in use or not in use. How many possibilities are therefore overall port usage of this computer? Determine possible outcomes of at least two ports

Answer 1

Let U be the random variable representing the number of ports in use at any given time. Also, let N be the random variable representing the number of ports not in use at any given time. The sample space is:

a) when all ports are not in use:{N,N,N,N}, then U=0

b) when 1 port is in use and 3 ports are not in use:{U,N,N,N}{N,U,N,N}{N,N,U,N}{N,N,N,U}, then U=1

c) when 2 ports are use and 3 ports not in use: {U,U,N,N} {U,N,U,N}{U,N,N,U}{N,U,N,U}{N,N,U,U}{N,U,U,N},then U=2

d) when 3 ports are in use and 1 port is not in use: {U,U,U,N}{U,U,N,U}{U,N,U,U}{N,U,U,U}, then U=3

e) when all 4 ports are in use:{U,U,U,U}, then U=4

The overall port usage has 16 possibilities.

The possible outcomes of at least 2 ports are:

When 2 ports are in use and 3 ports not in use: {U,U,N,N} {U,N,U,N}{U,N,N,U}{N,U,N,U}{N,N,U,U}{N,U,U,N},then U=2

When 3 ports are in use and 1 port is not in use: {U,U,U,N}{U,U,N,U}{U,N,U,U}{N,U,U,U}, then U=3

When all 4 ports are in use:{U,U,U,U}, then U=4

Therefore, there are 11/16 possible outcomes of at least 2 ports