Question

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?

Answer 1

1. What’s the probablity of a second person winning the small prize?
There are now 99 total marbles, and 24 silver marbles. So, 24/99 is 0.24 probability.
2. Which player is most likely to win a big prize?
Since each player draws a silver marble (aka a small prize) there are less small prize marbles in the bag after each turn. So, the first person would have a 5% chance (or 0.05)of winning the big prize gold marble, but the last person would have a slightly bigger chance (5.15% or 0.0515) of winning a big prize.
3. How could the game be made fair for each player?
Well it’s quite simple, just have each player return their marble and the number of marbles would be kept constant, giving everyone an equal chance. Or you could have them all play at the same time, either way.
4. Same answer as 3