You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: A piece of string is lying on the table. It is partially covered by three coins as seen in the figure. Under each coin the string is equally likely to pass over itself like this: <image1>
or like this: <image2>. What is the probability that the string is knotted after its ends are pulled?
<image3>
Choices:
(A) $\frac{1}{2}$
(B) $\frac{1}{4}$
(C) $\frac{1}{8}$
(D) $\frac{3}{4}$
(E) $\frac{3}{8}$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
B
Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: A piece of string is lying on the table. It is partially covered by three coins as seen in the figure. Under each coin the string is equally likely to pass over itself like this: <image1>
or like this: <image2>. What is the probability that the string is knotted after its ends are pulled?
<image3>
Choices:
(A) $\frac{1}{2}$
(B) $\frac{1}{4}$
(C) $\frac{1}{8}$
(D) $\frac{3}{4}$
(E) $\frac{3}{8}$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
val