Qumion #1 [8 marks] Consider the system below where component 1 is said to be connected in parallel with components 2 and 3 (while 2 and 3 are said to be connected in series). The system will only function properly if either component 1 works (W1) and/or components 2 and 3 work (W2 and W5), respectively. If component i, where i = {1,2, 3}, fails we will denote it with an Fa. [As an example, if the outcome is F1W2W5, then the system will function correctly since components 2 and 3 are working.] d i a. Answer each of the following (being sure to use set notation where applicable). i. List the elements of the sample space 5 (Le. all possible outcomes). ii. Suppose that A = {W1W3W;, W1W2F3, W1F2W3, W1F2F3,F1W3W3}. Describe event A in words. iii. Suppose that B is the event that exactly two components are working properly. State all possible outcomes in B. b. Are events A' and B mutually exclusive? Explain why or why not in the context of this problem. c. Suppose that the components function independently and P(W1) = 0.6, P(Wz) = 0.85, and P(Wa) = 0.9. i. Determine P(W1 n W: n W3) (i.e. the probability that components 1, 2, and 3 all work). Be sure to show all steps/formulas used in your calculation. ii. Determine the probability that the system functions properly. Be sure to show all steps/fonnulas used in your calculation