hi i need help please. I have figured out the answer to all the parts except part C (highlighted in the excel sheet). For this formula X + [(1-X) x X], how to solve and what is the correct answer? Im getting two conflicting answers: the textbook says .9783 and I think the teacher said .9891

the original question is this:

A B B E F G H J K L L M M N 1 a. Probability that both components will function, i.e., the system will function (Use Rule 1). Xx X = b. Probability that Backup for Component 1 & Switch both will function (Use Rule 1): XxX= Probability that Backup for Component 2 & Switch both will function (Use Rule 1): X X X = Rule 2): 3 4 5 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 Probability that Component 1 or (Backup for Component 1 & Switch) will function (Use 1 X + [(1-X)x X = Probability that Component 2 or (Backup for Component 2 & Switch) will function 2 (Use Rule 2%: X + [(1-X)x X] = Probability that both components will function, i.e., the system will work (Use Rule 1): XxX c. Probability that Backup for Component 1 & Switch both will function (Use Rule 1): XxX= Probability that Backup for Component 2 & Switch both will function (Use Rule 1): Xx X = Probability that Component 1 or (Backup for Component 1 & Switch) will function (Use 1 X + (1-X)x X] Probability that Component 2 or (Backup for Component 2 & Switch) will function (Use X + (1-X)x X] Rule 2): Rule 2): Probability that both components will function, i.e., the system will function (Use Rule 1): X+X= PROBLEMS 1. Consider the following system: .90 .90 Determine the probability that the system will operate under each of these conditions: a. The system as shown. b. Each system component has a backup with a probability of .90 and a switch that is 100 percent reliable. c. Backups with 90 probability and a switch that is 99 percent reliable