2. (Success of an event) Reliability analysis works not only in finding how the whole system is dependent on its multiple components, but makes sense in checking whether the desired event with several causes/ factors would happen. Suppose you want to learn how to bake during this quarantine, and the three important factors of a successful baking are ingredients, temperature and time. The ideal ingredients for the flour is cake flour, and you can also substitute it with a mixture of all-purpose flour and corn starch with certain ratio. Suppose you have sufficient cake flour w.p. p1, and sufficient all purpose flour and sufficient corn starch for the substitute mixture w.p. p2 and p3. After successfully preparing the ingredients, you hope to set up the right temperate and cook time for the oven. However, unfortunately there is something wrong with the oven's electronic display. Therefore w.p. p4 you set the temperature correctly and w.p. p5 you set the time appropriately. (a) Let A denote the event that you successfully bake the cake. Write A as a function of sub events described above by composing nested unions and intersections. Clearly define each of the subevents. (Hint: There should be 5 sub-events A1, A2, . . . A5.)

2. (Success of an event) Reliability analysis works not only in finding how the whole system is dependent on its multiple components, but makes sense in checking whether the desired event with several causes/ factors would happen. Suppose you want to learn how to bake during this quarantine, and the three important factors of a successful baking are ingredients, temperature and time. The ideal ingredients for the flour is cake flour, and you can also substitute it with a mixture of all-purpose flour and corn starch with certain ratio. Suppose you have sufficient cake flour w.p. p1, and sufficient all purpose flour and sufficient corn starch for the substitute mixture w.p. pa and p3. After successfully preparing the ingredients, you hope to set up the right temperate and cook time for the oven. However, unfortunately there is something wrong with the oven's electronic display. Therefore w.p. p you set the temperature correctly and w.p. p; you set the time appropriately. (a) Let A denote the event that you successfully bake the cake. Write A as a function of sub events de- scribed above by composing nested unions and intersections. Clearly define each of the subevents. (Hint: There should be 5 sub-events A1, A2, . .. As.)