Consider an expensive part with a reliability of $96\mathrm{.}6\%.$ If the part fails, it will cost the firm $$10,000.$

a$.$ What is the expected failure cost per part?

The probability of failure is $\%($round your response to two decimal places$).$

The expected failure cost per part is $ $($round your response to the nearest penny$).$

b$.$ On each part, a rather unreliable backup can be installed that has a reliability of just $35\mathrm{.}00\%.$ What is the per part to install the backup?

The new probability of failure is $\%($round your response to two decimal places$).$

The new expected cost of failure is $$($round your response to the nearest penny$).$

The firm should pay as much as $ for the backup $($round your response to the nearest penny$).$

c$.$ Suppose that a second $35\mathrm{.}00\%$ reliable backup part could be installed, so that if both the original and the used. If that second backup part costs $$110\mathrm{.}00,$ should it be installed? Support your answer.

The new probability of failure is $\%($round your response to two decimal places$).$

The new expected cost of failure is $ $($round your response to the nearest penny$).$

The firm should pay as much as $ for the backup $($round your response to the nearest penny$).$

Should the firm install the second backup?

Yes