Problem:
Probabilities Drawn from Large and Small Populations
A container holds a large number (> 10(0) of coins. They are divided into three types A, B, and C, which make up 20%, 30%, and 50% of the total.
(a) What are the probabilities P (A), P (B), P (C) of picking a coin of type A, B, or C if one coin is taken at random? What are the probabilities P(AB), P(AC), P(BC), P(AA), P(BB), P(CC), P(2 identical coins), P(2 different coins) for picking 2 coins?
(b) What are the probabilities if 10 coins (2 of type A, 3 of type B, and 5 of type C) are in the container?