1. Consider a fault tree with an AND gate under the top event. The first tier contains four failure events with respective failure probabilities of 0.005, 0.002, 0.01, and 0.0001.

a. What equation should you use to compute the probability of the top event?

b. Using the equation, what numerical value do you get for the top event probability?

c. For the top event, what is the probability of the complimentary event (i.e., success probability)?

2. A professor scheduled a test at 11 a.m. on Wednesday. A student might fail to show up for the test.

a. If you want to make a fault tree for this, what text would you put in the top event box?

b. What type of gate would you put in the top event box?

c. List reasons for this "no-show."

d. Group the reasons for no-show into categories for placing under the gate in a fault tree. If you have more than five reasons, consider consolidating some of the reasons into categories suitable for a fault tree.

e. Use the outline format to write the final version of the logic you would use to make a fault tree for the student failing to show up for the test.