An electrical panel has three toggle switches labeled I, II$,$ III, each if which can be either on $($O$)$ or off $($F$).$ a$)$ Construct a tree to represent the possible configurations for these three switches. b$)$ List the elements of the sample space generated by the tree. c$)$ List the sample points that constitute the events A: at least one switch is on$,$ B: switch I is on$,$ C: no switch is on$,$ D: four switches are on$.$ d$)$ Are events A and B mutually exclusive? Are events A and C mutually exclusive? Are events A and D mutually exclusive?