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A distribution of voters is uniform over [0, 1]. Candidates A and B have already entered the election and have chosen positions at 1/4 and 3/4, respectively.
-If C enters at 1/3, what fraction of the vote does the winner receive?

Question

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First, we need to determine who the winner is. If C enters at 1/3, then the candidate closest to the center (1/2) will win. In this case, candidate A is 1/4 away from the center and candidate B is 1/4 away from the other side of the center, so candidate A will win.

Next, we need to determine what fraction of the vote the winner receives. Since the distribution of voters is uniform, each candidate will receive a fraction of the vote equal to the length of the interval they occupy. 
Candidate A occupies an interval of length 1/4.
Candidate B occupies an interval of length 1/4.
Candidate C occupies an interval of length 1/3.

Therefore, the winner (candidate A) receives a fraction of the vote equal to 1/4.

Answer choice C) 11/24 is the only option less than 1/2 (since candidate A occupies less than half the interval) and greater than 1/4 (since candidate C's interval is greater than candidate A's interval). Therefore, the correct answer is C) 11/24.

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