Applications of Probability — Test

Question 10 • Concepts in Probability and Statistics

Which of the following is a valid probability distribution?

Answer

Image with description The bar graph is titled Probability Distribution A. The horizontal axis lists 0 to 6 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 3 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 6 bars on the graph, and all the bars have a uniform height of 0 point 2.

Image with description The bar graph is titled Probability Distribution B. The horizontal axis lists 0 to 6 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 4 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 6 bars on the graph. The first bar is at 1 and its height is 0 point 1, the second bar is at 2 and its height is 0 point 2, the 3rd bar is at 3 and its height is 0 point 3, the 4th bar is at 4 and its height is 0 point 3, the 5th bar is at 5 and its height is 0 point 2, and the 6th bar is at 6 and its height is 0 point 1.

Image with description The bar graph is titled as "Probability Distribution D". The horizontal axis ranges from 0 to 6 with increments of 1 and also labeled as X. The vertical axis ranges from 0 to 0 point 6 with increments of 0 point 1 and also labeled as a P subscript X of x. There are 5 bars on the coordinate plane. The first bar is located at 1 and its height is 0 point 2, the second bar is located at 2 and its height is 0 point 1, the third bar is located at 3 and its height is 0 point 1, the fourth bar is located at 4 and its height is 0 point 5, and the fifth bar is located at 6 and its height is 0 point 1.

Image with description The bar graph is titled Probability Distribution C. The horizontal axis lists 0 to 6 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 5 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 5 bars on the graph. The first bar is at 1 and its height is 0 point 1, the second bar is at 2 and its height is 0 point 2, the 3rd bar is at 3 and its height is 0 point 4, the 4th bar is at 5 and its height is 0 point 1, and the 5th bar is at 6 and its height is 0 point 1.

Explanation

A valid probability distribution must assign nonnegative probabilities that add up to 1. For choice D, the bar heights sum to 0.2 + 0.1 + 0.1 + 0.5 + 0.1 = 1.0, so it is a valid probability distribution.

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