1. A mainframe computer has 16 ports. At any given time, each port is either in use or not in use. How many possibilities are there for overall port usage of this computer? How many of these entail the use of at least one port?

2. A flashlight operates on two batteries. Eight batteries are available but three are dead. In a random selection of batteries, what is the probability that exactly one dead battery will be selected? 25. 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?