3/16 should be the correct answer.
Maximum Possible Waiting Time = 8 + 8 = 16 mins.
Minimum Possible Waiting Time = 0 + 0 = 0 mins.
Given that, at both the stations B & C, any waiting time up to 8 minute is equally likely.
So any waiting time between 0 to 16 should be equally likely.
Now the problem can be thought as "Choosing any point P randomly on real number line between 0 to 16(inclusive), what is the probability that the point will lie between 13 to 16."
Point P will represent our total waiting time, clearly all points will be equally likely since they will be equidistant from each other.
The Probability that P > 13 = length of line segment between 13 and 16 / length of line segment between 0 and 16
Hence the probability that total waiting time is greater than 13 minutes = (16 - 13) / (16 - 0) = 3/16
Manish will arrive late at D if he will spend more than 13 minutes in waiting.
So the probability that Manish will arrive late at D = 3/16.