(a)[1]
A student must be picked at random from a group of three. Explain how one fair throw of a six-sided dice could be used to decide which student is chosen.
(b)[5]
The times, measured in minutes, that students take to finish a test are normally distributed with mean $125$ and variance $50$. If two students are selected at random, find the probability that the difference between their completion times is more than $12$ minutes.