A spinner has two equal sections, one green and one orange. The spinner is spun three times, resulting in the sample space cap s is equal to GGG, GGO, GOG, OGG, GOO, OGO, OOG, OOO If the random variable cap x represents the number of times orange, cap o , is spun, which graph represents the probability distribution?
Answer
A
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 3 in increments of 1 and is labeled as x. The vertical axis lists 0 to 3 point 5 in increments of 0 point 5 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 0, with its height at 1. The second bar is at 1, and its height is 3. The 3rd bar is at 2, and its height is 3; the 4th bar is at 3, and its height is 1.
B
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 3 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 6 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 0 and its height is 0 point 1 2, the second bar is at 1 and its height is 0 point 5, the 3rd bar is at 2 and its height is 0 point 2 5, and the 4th bar is at 3 and its height is 0 point 1 2.
C
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 3 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 4 0 in increments of 0 point 0 5 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 0; its height is 0 point 1 3. The second bar is at 1; its height is 0, point 3 8. The 3rd bar is at 2, its height is 0 point 3 8, and the 4th bar is at 3, and its height is 0 point 1 2.
D
Image with description The bar graph is titled probability distribution. The horizontal axis lists 0 to 3 in increments of 1 and is labeled as x. The vertical axis lists 0 to 0 point 6 in increments of 0 point 1 and is labeled as a P subscript x of x. There are 4 bars on the graph. The first bar is at 0, and its height is 0 point 1 2. The second bar is at 1, its height is 0 point 2 5, the 3rd bar is at 2, and its height is 0 point 5; and the 4th bar is at 3, and its height is 0 point 1 2.
Explanation
Each of the three spins has two equally likely outcomes, so there are 8 equally likely sequences. For 0, 1, 2, or 3 orange results, the counts of sequences are 1, 3, 3, and 1, giving probabilities 1/8, 3/8, 3/8, and 1/8 (about 0.13, 0.38, 0.38, and 0.13). Choice D shows these probabilities, rounded to the displayed values.
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