An organization dedicated to ensuring fairness in television game shows is investigating Wheel of Fortune. In this show, three contestants are required to solve puzzles by selecting letters. Each contestant gets to select the first letter and continues selecting until he or she chooses a letter that is not in the hidden word, phrase, or name. The order of contestants is random. However, contestant 1 gets to start game

1, contestant 2 starts game 2, and so on. The contestant who wins the most money is declared the winner and he or she is given an opportunity to win a grand prize. Usually, more than three games are played per show, and as a result it appears that contestant 1 has an advantage: contestant 1 will start two games, whereas contestant 3 will usually start only one game. To see whether this is the case, a random sample of 30 shows was taken and the starting position of the winning contestant for each show was recorded. These are shown in the following table:

Do the tabulated results allow us to conclude that the game isunfair?

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Starting position 2 3 Number of wins 14 10 6