When a machine is improperly adjusted, it has probability 0.2 of producing a defective item. Each day the machine is run until 5 defective items are produced. If this occurs, the machine is stopped and checked for adjustment.
a) What is the probabiliy that an improperly adjusted machine will produce 8 or more items before being stopped?
b) What is the average number of items an improperly adjusted machine will produce before being stopped?