Please show work Consider an expensive part with a reliability of $97\mathrm{.}4\%.$ 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 $30\mathrm{.}00\%.$ What is the maximum

amount that the firm should be willing to pay 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 $30\mathrm{.}00\%$ reliable backup part could be installed, so that if both the original and the first backup

part fail, then the second backup part will be used. If that second backup part costs $$120\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

No