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Question 10 • Algebra 2 with Probability

A six-sided number cube is considered "loaded” if it is not fair. Which of the following could be the probability distribution for a loaded number cube?

Answer

Table with 6 columns and 2 rows.Row 1: Column 1, '1'; Column 2, '2'; Column 3, '3'; Column 4, '4'; Column 5, '5'; Column 6, '6' Row 2: Column 1, '0 point 2 0'; Column 2, '0 point 1 5'; Column 3, '0 point 2 0'; Column 4, '0 point 2 0'; Column 5, '0 point 2 0'; Column 6, '0 point 2 0'

Table with 6 columns and 2 rows.Row 1: Column 1, '1'; Column 2, '2'; Column 3, '3'; Column 4, '4'; Column 5, '5'; Column 6, '6' Row 2: Column 1, '0 point 0 5'; Column 2, '0 point 1 2'; Column 3, '0 point 2 3'; Column 4, '0 point 1 0'; Column 5, '0 point 2 4'; Column 6, '0 point 2 6'

Table with 6 columns and 2 rows.Row 1: Column 1, '1'; Column 2, '2'; Column 3, '3'; Column 4, '4'; Column 5, '5'; Column 6, '6' Row 2: Column 1, '1 sixth'; Column 2, '1 sixth'; Column 3, '1 sixth'; Column 4, '1 sixth'; Column 5, '1 sixth'; Column 6, '1 sixth'

Table with 6 columns and 2 rows.Row 1: Column 1, '1'; Column 2, '2'; Column 3, '3'; Column 4, '4'; Column 5, '5'; Column 6, '6' Row 2: Column 1, '0 point 2 0'; Column 2, 'negative 0 point 1 0'; Column 3, '0 point 2 5'; Column 4, '0 point 1 5'; Column 5, '0 point 3 0'; Column 6, '0 point 2 0'

Explanation

A probability distribution must have probabilities that are all nonnegative and add up to 1. In choice B, 0.05 + 0.12 + 0.23 + 0.10 + 0.24 + 0.26 = 1, and the probabilities are not all equal, so it could describe a loaded number cube.

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