Suppose that there are n CPUs on a common bus. The probability that any CPU tries to use the bus in a given cycle is p. What is the chance that: a. The bus is idle (0 requests).
b. Exactly one request is made.
c. More than one request is made.

a) ( 1 - P )^n

b) nP ( 1 - p )^n-1

c) 1 - p ( 1 - p )^n-1  -  ( 1 - p )^n-1

Explanation:

A) Chance that the bus is idle

For the bus to be idle, the CPU has to be idle as well and the probability of an idle CPU is = 1 - P .therefore The chance that the bus is idle all N numbers of CPU's are idle/silent  =  ( 1 - P )^n

B) Chance that exactly one request is made

probability in the CPU when a single request is made can be expressed as :

P ( 1 - p ) ^n-1

probability that a single request is made to the Bus due to the single request made to N number of CPU's = nP ( 1 - p )^n-1

C) chance the more than one request is made

= 1 - p ( 1 - p )^n-1  -  ( 1 - p )^n-1

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