Question

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

Answer 1

here is the sample space for throwing two die
{ 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 }
(Two) fair dice are rolled, and the product of the two numbers is recorded. Which of the following best describes the theoretical probability distribution? uniform symmetric negatively skewed positively skewed Uniform Symmetry -> Sequence of answers that increase or decrease by the same amount Negative Skew = Large # -> Small # Positive Skew = Small # -> Large #

Answer 2

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.