Biased Random Number Generator

Question

I am looking for a random number generator that can be biased. For instance, say I want a random number between 1-5, with the probability being:

1: Comes up 20% of t

Answer 1

Throw a random real number x in [0,1], if 0< x<0.2 return 1, if 0.2, etc.

See here for the general problem.