Loosing Your Marbles?
A hat contains two blue marbles and three red marbles. If you draw a blue marble, you win $1. If you draw a red marble, you lose $1.
Question 1: Would you play this game if you get just one draw, i.e. is the game either fair or biased in your favor?
Question 2: Would you play this game if you may draw, without replacement, until you decide to quit or the hat runs out of marbles?
Question 3: What are the expected values in both cases?
Source: A problem that was sent by email around our Math Department.
Hint: Gather a hat with two blue marbles (chips?) and three red marbles (chips?). Now, simulate the problem situation until you get a feel for a good way to approach a solution.
Solution Commentary: First, the game is not a good one if you only get one draw. Because of the higher probability of drawing a red marble, the expected value is (2/5)*($1) + (3/5)*($1) = $0.20.
John W. of our department offered this solution for the second case: Make the first draw and then stop as soon as (number of blues drawn  number of reds drawn) is greater than or equal to 0. Your expected take in this case is $0.20. That is, stop when the sequence of draws shows B, RB, RRBB, RRBRB, or RRRBB.
Do you agree with his logic and claim?
