Suppose you have three computers in your apartment/house and that
your ISP has allocated 5 IP addresses for your apartment/house.
Suppose further that, for some inexplicable reason, rather than
assign an IP address to each computer, your ISP selects an IP
address at random (each of which has a probability of \(1/5\)
of being selected) and assigns it to a computer each time the
computer is turned on. Since your ISP does not keep track of which IP
addresses it has assigned, it might assign the same IP address to more
than one computer.
Suppose two computers are turned on. What is the probability that they
will have the same IP address?
Suppose all three computers are turned on. What is the probability that
any two will have the same IP address? Intuitievly, why does it make sense
that your answer to this part of this question is larger than your answer
to the previous part of this question?