A carnival game allows a group of players to each draw and keep a marble from a bag. The bag contains 5 gold marbles, 25 silver marbles, and 70 red marbles.
A player wins a large prize for drawing a gold marble and a small prize for drawing a silver marble. There is no prize for drawing a red marble.
At the start of the game, the probability of winning a large prize is 0.05 and the probability of winning a small prize is 0.25.
Suppose that the first player draws a silver marble and wins a small prize. What is the probability that the second player will also win a small prize?
If a group of four plays the game one at a time and everyone wins a small prize, which player had the greatest probability of winning a large prize?
How could the game be made fair for each player? That is, how could you change the game so that each player has an equal chance of winning a prize?