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Probability of only one CPU using the bus.

In a n-CPU shared bus system,if Z is the probability that any CPU requests the bus in a given cycle,the probability that only one CPU uses the bus is given by-

Options :

(1) nZ(1-Z)(n-1)

(2) Z(1-Z)(n-1)

(3) nZ(1-Z)n

(4) (n-1)Z(1-Z)n.

5Comments
Arul @innovwelt
12 Mar 2016 12:04 am

check with the answer.

Let us say the CPUs are C1, C2, ... Cn.

the probability that only one CPU uses the bus

= P((C1 requests the bus) & (except C1, other CPUs do not request the bus)) +

    P((C2 requests the bus) & (except C2, other CPUs do not request the bus)) +

    .....

  = nZ(1-Z)n-1

Jitendra Verma @jitendraverm
12 Mar 2016 12:08 am

Great explanation sir!!! Thanks 

Pritam Prasun @pritam
12 Mar 2016 12:10 am

EDIT: Above explanation is correct. Thanks Arul.

Jitendra Verma @jitendraverm
12 Mar 2016 12:10 am

Correct answer is (1).

Deepesh Kataria @deepesh3092
22 Mar 2016 11:36 pm

SIMPLY THINK.....this way ..

the probability will be Z(1-Z)n-1 ...that is one get bus and others dont ..

now this one can can be any CPU=CPU1 or CPU2 or ...CPUN

                                                        =NZ(1-Z)n-1