at the second step each of those can send to four servers at

at the second step; each of those can send to four servers at the

third step; and then the message goes to the recipient’s server.

(a) How many paths are possible?

(b) If all paths are equally likely, what is the probability that a

message passes through the first of four servers at the

third step?

Solution

The number of servers in first step = 5

The number of servers in second step = 5, and

Number of servers in third step = 4.

a)

So, the total number of paths will be the multiplication of all the possible paths = 5 x 5 x 4 = 100

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(b)

If, the message has to pass through the first server in third step, then the number of possible paths = 5 x 5 x 1 = 25.

So, the required probability would be = 25/100 = 1/4 = 0.25