Question 15
Alex has a fair six-faced die with the fractions $\frac12$, $\frac32$, $\frac52$, $\frac72$, $\frac92$ and $\frac{11}2$ on its faces. Ben, on the other hand, has a spinning wheel, that is divided into $n$ equal parts. An integer from $0$ to $n-1$ is written on each part, with each number appearing exactly once.
Alex rolls his die, and Ben spins his wheel at the same time. Let $p$ be the probability that Ben obtains a greater number than the one Alex obtains. What is the smallest value of $n$ for which $p$ is at least $\frac12$?
Original response line:
Alex rolls his die, and Ben spins his wheel at the same time. Let $p$ be the probability that Ben obtains a greater number than the one Alex obtains. What is the smallest value of $n$ for which $p$ is at least $\frac12$?
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