Two fair dice are rolled, and the product of the two numbers is recorded. Which of the following best describes the theoretical probability distribution?

A.) uniform

B.) symmetric

C.) negatively skewed

D.) positively skewed

The best answer is:

A) uniform.

Explanation:

The sample space for the product of two dice is:

{1, 2, 3, 4, 5, 6

2, 4, 6, 8, 10, 12

3, 6, 9, 12, 15, 18

4, 8, 12, 16, 20, 24

5, 10, 15, 20, 25, 30

6, 12, 18, 24, 30, 36}

Using this, the theoretical probabilities are:

P (1) = 1/36

P (2) = 2/36

P (3) = 2/36

P (4) = 3/36

P (5) = 2/36

P (6) = 3/36

P (8) = 2/36

P (9) = 1/36

P (10) = 2/36

P (12) = 4/36

P (15) = 2/36

P (16) = 1/36

P (18) = 2/36

P (20) = 2/36

P (24) = 2/36

P (25) = 1/36

P (30) = 2/36

P (36) = 1/36

If a bar graph is drawn to represent this, we see that this is close to uniform.

It is not exactly uniform, but it is definitely not symmetric; not positively skewed; and not negatively skewed.

We can derive the sample space from this for the products. In this problem, we get

{ 1, 2, 3, 4, 5, 6,

2, 4, 6, 8, 10, 12,

3, 6, 9, 12, 15, 18,

4, 8, 12, 16, 20, 24,

5, 10, 15, 20, 25, 30,

6, 12, 18, 24, 30,36 }

In these sets, we can see that the probability is positively skewed