In a game show, contestants are given the opportunity win a new car if they correctly choose the winning door three times in a row. In the first round, they must choose between 3 doors, one of which is labeled "win." In the second round and third rounds, they will choose from 2 doors, with one labeled "win." Their options are shown in the tree diagram below. Three flowcharts indicate the options behind doors 1, 2, and 3. In the first flowchart, door number 1 is Lose, and branches off to win and to lose for door number 2. Door number 3 has two additional options of win or lose under both options in door number 2. The second flowchart has Win behind door number 1 and the third chart has Lose behind door number 1. The second and third doors are identical in all three charts. In the first round there is a one in three chance of choosing the "win" door, and in the second and third rounds there is a one in two chance of choosing the "win" door. They are blind folded, and are not given an opportunity to see the doors beforehand. What is the probability that a contestant will NOT win a new car? Select the correct answer below:
