Question 57
We have two concentric circles $C_{1}$ and $C_{2}$ with radii $1$ and $2$, respectively. A random chord of $C_{2}$ is chosen. What is the probability that it intersects $C_{1}$?
Your answer to this problem must be expressed in the form $\frac{m}{n}$, where $m$ and $n$ are positive integers. If your answer is in this form, your score for this problem will be $\left\lfloor\frac{25 \cdot X}{Y}\right\rfloor$, where $X$ is the total number of teams who submit the answer $\frac{m}{n}$ (including your own team), and $Y$ is the total number of teams who submit a valid answer. Otherwise, your score is $0$. (Your answer is not graded based on correctness, whether your fraction is in lowest terms, whether it is at most $1$, etc.)
Your answer to this problem must be expressed in the form $\frac{m}{n}$, where $m$ and $n$ are positive integers. If your answer is in this form, your score for this problem will be $\left\lfloor\frac{25 \cdot X}{Y}\right\rfloor$, where $X$ is the total number of teams who submit the answer $\frac{m}{n}$ (including your own team), and $Y$ is the total number of teams who submit a valid answer. Otherwise, your score is $0$. (Your answer is not graded based on correctness, whether your fraction is in lowest terms, whether it is at most $1$, etc.)