Question

For this assignment, explicitly state the five steps of a stimulation and carry out the simulation. For the first problem, use a calculator. For the second, use the random digit table.

A nuclear reactor facility has two separate safety systems in place to prevent a nuclear meltdown. They prevent a meltdown by shutting down the reactor when the temperature reaches the danger level. The first system shuts down the reactor 80% of the time when the danger level is reached. The second system (which is completely separate from the first) shuts down the reactor 90% of the time when the danger level is reached.

a. Use your calculator to do 10 repetitions with the first system alone. Theoretically, it should successfully shut it down 16 out of 20 times.

b. Use your calculator to do 10 repetitions with the second system alone. Theoretically, it should successfully shut it down 18 out of 20 times.

c. Use your calculator to do 20 repetitions with the first and second systems working together. The reactor will successfully shut down if one or both systems are not working.

Answer 1

A nuclear reactor facility

a. Suppose you have a 10-sided die. If you roll it when the system is not working and get either 1 or 2, then the first system fails to shut the reactor down. If you actually rolled the die 20 times, then theoretically 16 times you'll see 3-10, and 4 times you'll see 1 or 2.

b. Suppose you have the same 10-sided die. If you roll it and the die shows 1, then the second system failed to shut the reactor down. You should see the dice roll 2-10 about 18 times and the 1 show up twice.

c. Now, take both dice and roll them together (supposing they're different colors so you know which reactor is which). You'll need 40 dice rolls. if the system one dice roll gives you a 1 or 2, then that system did not shut the reactor down. If the second die shows a 1, then that system did not shut down the reactor.

Since you're using a calculator instead of dice. use the randint() command 40 times. Write the results down in two columns of 20 each. This will give you a list of results that you can use to verify you're close to what you expect to see. You MIGHT see a single incident where at least one of the systems didn't shut down the reactor.

The probability that the first system doesn't shut down the reactor is 20%. The probability that the second system doesn't shut down the reactor is 10%. The probability that neither system shuts down the reactor is .2(.1) = .02.

If you insist on using 1-100 instead of 1-10, then you'll need to recall that the first system fails with numbers 1-10 and the second system fails with numbers 1-20.