## Invitation to Computer Science 8th Edition

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.
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.