An electrical control panel has three toggle switches labeled I, II, and III each of which can be either on (0) 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?
(e) What is the name given to an event such as 0?
(f) If, at any given time, each switch is just as likely to be on as off, what is the probability that no switch is on?