CSC 221: Computer Programming I
Spring 2008
HW7: Marble Jar Simulations
In this assignment, you will make use of previously defined Java classes
to help solve two brain-teaser puzzles. These puzzles, which are common among
statisticians and discrete mathematicians, involve drawing black and
white marbles from a jar.
- Suppose a jar contains the same number of black and white marbles.
If you reach in and pull out two random marbles, are they more likely to be the
same color or different colors?
- Suppose a jar has an arbitrary mixture of black and white marbles.
As long as there are at least two marbles in the jar, draw two random marbles and:
- If they are the same color, throw them both away and add a brand new black
marble to the jar.
- If they are different colors, throw away the black one and return the white
marble to the jar.
Can the marble drawing process go on forever? Furthermore, if you are told
the initial contents of the jar, can you predict the final outcome?
PART 1: PuzzleOne
The MarbleJar and
PuzzleOne classes have been provided for you.
- Based on simulation results using these classes, what is the answer to this puzzle?
Are the two marbles more likely to be same color or different colors?
Can you explain why?
- Does increasing the total number of marbles in the jar affect the answer
in any way?
PART 2: PuzzleTwo
Design and implement a class named PuzzleTwo that can be used to
simulate the steps in the second puzzle. The user should be able to somehow
specify the number of black and white marbles in the jar, then view the steps
in the simulation. As each pair of marbles is drawn, a message describing the
action taking place (including its number in the process), should be printed.
The simulation should stop if fewer than two marbles remain in the jar.
For example, the output produced by the method should look like the following:
<![CDATA[
1: I drew black and white -- replacing a white marble.
2: I drew white and white -- replacing a black marble.
3: I drew white and black -- replacing a white marble.
4: I drew white and black -- replacing a white marble.
.
.
.
18: I drew black and white -- replacing a white marble.
19: Only one marble left... it is white.
]]>
- Based on repeated simulation results, what is the answer to this puzzle?
Can the process of drawing and replacing marbles go on forever? Why or why not?
- If you know the initial contents of the jar, can you predict the final
outcome? Explain.