Problems $17\mathrm{.}1-17\mathrm{.}17$ relate to Reliability

$17\mathrm{.}1$ The Beta II computer's electronic processing unit contains $50$ components in series. The average reliability of each component is $99\mathrm{.}0\%.$ Using Figure $17\mathrm{.}2,$ determine the overall reliability of the processing unit.

SOLVED PROBLEM $17\mathrm{.}2$

A recent engineering change at Sullivan Wrist Calculator places a backup component in each of the two least reliable transistor circuits. The new circuits will look like the following:

What is the reliability of the new system?

$]=[\mathrm{.}9+(1-\mathrm{.}9)\mathrm{.}9]\mathrm{.}95\mathrm{.}98[\mathrm{.}9+(1-\mathrm{.}9)\mathrm{.}9]\mathrm{.}99[\mathrm{.}903$