Answer
If there is one chance in four that a program is blocked waiting for
input/output, then there is a (1/4) $\times(1 / 4)=1$ chance in 16 that both of
the two programs in memory are simultaneously blocked waiting for I/O.
Therefore, the processor will be busy $15 / 16,$ or about 94$\% $, of the time.
This is processor utilization. If we increase the number of programs
in memory to four, then the probability that all four of these programs
are blocked at the same time waiting for 1$/ 0$ is $(1 / 4) \times(1 / 4) \times(1 / 4) \times$
$(1 / 4)=1$ chance in $256 .$ Now the utilization of the processor is 255$/ 256$ ,
or about 99.6$\%$ . We can see clearly now why it is helpful to have more
programs in memory. It increases the likelihood that at least one program
will always be ready to run.
Work Step by Step
If there is one chance in four that a program is blocked waiting for
input/output, then there is a (1/4) $\times(1 / 4)=1$ chance in 16 that both of
the two programs in memory are simultaneously blocked waiting for I/O.
Therefore, the processor will be busy $15 / 16,$ or about 94$\% $, of the time.
This is processor utilization. If we increase the number of programs
in memory to four, then the probability that all four of these programs
are blocked at the same time waiting for 1$/ 0$ is $(1 / 4) \times(1 / 4) \times(1 / 4) \times$
$(1 / 4)=1$ chance in $256 .$ Now the utilization of the processor is 255$/ 256$ ,
or about 99.6$\%$ . We can see clearly now why it is helpful to have more
programs in memory. It increases the likelihood that at least one program
will always be ready to run.
