IT 223: Data Analysis
Solutions to Assignment 4
Marble Jar Problems
The following problems refer to a marble jar
which has 10 red marbles, 15 black marbles and 25 white marbles.
- What is the chance of
drawing a red marble?
10 /
(10+15+25) = 1/5
- What is the chance of
drawing a white marble, replacing it and drawing a white marble again?
25/50
* 25/50 = 0.25
- What is the chance of
drawing a white marble twice without replacing it between draws?
25/50
* 24/49 = 0.245
- What is the chance of not
drawing a black marble?
(10
+ 25) / 50 = 35/50
- Three draws are performed in a row, replacing the drawn
marble each time. What is the chance that none of the three draws were a
black marble?
35/50
* 35/50 * 35/50 = .343
- Three draws are performed in a row, replacing the drawn
marble each time. What is the chance that at least one of the three draws were
a black marble? (hint: use your answer in the last question to answer this
question)
This is the complement (opposite)
of the last problem: 1 - .343 = .657
Dice problems
- Assume that a pair of
5-sided dice is rolled. List all of the possible rolls to answer the
remaining questions.
1 1 1
2 1 3 1
4 1 5
2 1 2
2 2 3 2
4 2 5
3 1 3
2 3 3 3
4 3 5
4 1 4
2 4 3 4
4 4 5
5 1 5
2 5 3 5
4 5 5
- What is the chance of
throwing doubles (each die has the same value)? 5/25
- What is the chance of
rolling a sum of 4? 3 / 25
- What is the chance of
rolling a sum of at least 8? There are 6 ways to throw 8 or higher: 6 / 25