For "Maintenance and Reliability", you can pick up one question from Q$1$ and Q$2.$

For "Monte Carlo simulation", you can pick up one question from Q$3$ and Q$4.$

Maintenance and Reliability:

$1.$ The Beta II computer$$s electronic processing unit contains $50$ components in series. The average reliability of each component is $99\mathrm{.}0\%.$ Using the Figure of $[$Average reliability of each component $($percent$)],$ determine the overall reliability of the processing unit.

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$2.$ What are the expected number of yearly breakdowns for the power generator at Orlando Utilities that has exhibited the following data over the past $20$ years?

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Monte Carlo simulation:

$3.$ The daily demand for tuna sandwiches at an Ohio University cafeteria vending machine is $8,9,10,$ or $11,$ with probabilities $0\mathrm{.}4,0\mathrm{.}3,0\mathrm{.}2,$ or $0\mathrm{.}1,$ respectively. Assume the following random numbers have been generated: $09,55,73,67,53,59,04,23,88,$ and $84.$ Using these numbers, generate daily sandwich sales for $10$ days.

$4.$ The table below shows the partial results of a Monte Carlo simulation. Assume that the simulation began at $8$:$00$ a$.$m$.,$ and there is only one server.

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a$)$ When does service begin for customer number $3?$

b$)$ When will customer number $5$ leave?

c$)$ What is the average waiting time in line?

d$)$ What is the average time in the system?