Question

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.

Answer 1

a) ( 1 - P )^n

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

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

Step-by-step 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