The Walton-Draper Company has just received a large shipment of noise canceling headphones from its main supplier. Its quality control people have devised a plan for evaluating the shipment by selecting a few items and subjecting them to rigorous testing. More specifcally, an inspector will select one item and test it. If this item fails the test (that is, if it is identifed as deective), the company will send back the entire shipment. If it passes, the inspector will take a second item to test. If this fails the test, the company will send back the entire shipment. Otherwise, the inspector will take a third item, etc. Such testing will continue up to a maximum of fve items. If all fve items pass inspection, the company will accept the entire shipment. IF the shipment contains just 3% defective items,
a. How likely is it that the inspector will need to test exactly three items before she reaches the decision to send back the shipment?
b. How likely is it that the inspector will eventually decide to accept the shipment?
c. How likely is it that the inspector will need to test AT LEAST three items before she reaches a decision either to accept or send back the shipment?