Buses arrive at ten minute intervals starting at noon. A man arrives at the bus stop at a random time $X$ minutes after noon, where $X$ has the CDF $F_X(x)$:
\begin{cases}
0 & x< 0 \\
\frac{x}{60} & 0\leq x\leq 60 \\
1 & 60> x
\end{cases}
What is the probability that he waits less than five minutes for a bus?
This implies that his time of arrival is uniformly distributed. Will the result be simply $5/60$?
Best Answer
Given that the buses arrive every $10$ minutes, the buses arrive $6$ times within an hour time.
The man arrives uniformly at any minute within an hour, so it is also uniform within a $10$-minute interval. The probability he waits for less than $5$ minutes is therefore $1/2$.