MadeEasy Test Series: Operating System - Process

Question

Q. A process spends 25% of its time waiting for I/O to complete. if 3 process in memory at a time, then the probability of CPU utilized(assume all I/O process are overlapped)  is......................

so here 2 solution plz check first one why not correct

1.    1 -  [ (3C1 *(.25)* (.75)^2  + (3C2 *(.25)^2* (.75) + (3C3 *(.25)^3* )

2.   1  -  [ (3C3 *(.25)^3* ) ]

Comments

3 process in memory at a time . and in 1st approch you consider 1st + 2nd and 3rd seperate.

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I think 100% utillization because 9 parts of CPU utilization and 3 parts of IO overlapped with any of the 9 parts of CPu utilization.

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kk thks

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I dont know what they mean by "assume all I/O process are overlapped". Overlapped with each other, or overlapped with CPU cycles. Also problem does not specify any sort of probability. It specified 25% of total execution time spent for IO. But thats not probability of anything right? We cannot use it / interprete as probability, right?

Process spends 25% in IO $\neq$ 25% Probability that process spends in IO

Process spends 25% in IO at 100% probability as this is a given fact.

Somehow I feel instead of asking for probability it should have asked for percentage of CPU utilized. ??? :\

Answer 1

Given that the process spends 25% of its time waiting for I/O to complete, it means that 75% of its time is spent on CPU-bound tasks. Therefore, the CPU utilization for each process is 75%.

Since there are 3 processes in memory at a time, the CPU utilization for the system as a whole is the sum of the individual CPU utilizations divided by the number of processes:

CPU utilization=CPU utilization per process×Number of processesTotal number of processes in memoryCPU utilization=Total number of processes in memoryCPU utilization per process×Number of processes​

Substituting the values, we get:

CPU utilization=0.75×33=0.75CPU utilization=30.75×3​=0.75

So, the probability of CPU utilization is 0.750.75 or 75%75%.