Question

The sides of a fair cubical die are numbered 2, 3, 3, 4, 4, and 5. The die is thrown twice and the outcomes are added to give a total T. Construct a table for the probability distribution of T.

Answer 1

The Probability Distribution of the Sum of Two Dice Rolls

Total (T) Probability

4 1/36

5 2/36

6 3/36

7 5/36

8 6/36

9 5/36

10 3/36

11 2/36

12 1/36

How to solve

Each die has 6 possible outcomes.

Since the dice are thrown twice, the total number of possible outcomes is 6 x 6 = 36.

We need to calculate the number of ways to get each sum from 4 to 12.

For T = 4, there is only one way: (2, 2).

For T = 5, there are two ways: (2, 3) and (3, 2).

Similarly, we can calculate the number of ways for each sum.

Finally, we divide the number of ways for each sum by the total number of possibilities (36) to get the probability.