Question

the following segmented bar graph shows whether adults and children enjoy riding roller coasters at least once a year. roller coaster opinion adults children enjoy do not enjoy how many more times likely are children to enjoy riding roller coasters at least once a year than are adults? 4 times more likely 2.5 times more likely 3.75 times more likely 3.2 times more likely

Explanation:

Step1: Analyze the bar graph

Assume each small segment (the vertical lines at the top) represents a unit. For Adults: "Enjoy" (orange) has 8 units, "Do not Enjoy" (blue) has 2 units. Total adults: \(8 + 2=10\). Probability adults enjoy: \(\frac{8}{10} = 0.8\). For Children: "Enjoy" (blue) has 8 units, "Do not Enjoy" (orange) has 2 units? Wait, no, looking at the graph: Adults' "Enjoy" (orange) is 8, "Do not" (blue) is 2. Children's "Enjoy" (blue) is 8, "Do not" (orange) is 2? Wait, no, maybe the segments: Let's count the number of segments for "Enjoy" in each group. Adults: Enjoy (orange) has 8 parts, Do not (blue) has 2 parts. Children: Enjoy (blue) has 8 parts, Do not (orange) has 2 parts? Wait, no, maybe the length: Adults' Enjoy bar (orange) is 8 units, Do not (blue) is 2 units. Children's Enjoy bar (blue) is 8 units, Do not (orange) is 2 units? Wait, no, the question is "how many times more likely", so we calculate the probability of children enjoying divided by probability of adults enjoying. Wait, maybe the counts: Let's say the number of adults who enjoy is 8, do not enjoy is 2 (total 10). Number of children who enjoy is 8, do not enjoy is 2? No, that can't be. Wait, maybe the graph: Adults: Enjoy (orange) is 8, Do not (blue) is 2. Children: Enjoy (blue) is 8, Do not (orange) is 2? Wait, no, maybe the "Enjoy" for children is 8, "Do not" is 2, and for adults "Enjoy" is 2, "Do not" is 8? Wait, the colors: Adults: blue is "Do not Enjoy", orange is "Enjoy". Children: blue is "Enjoy", orange is "Do not Enjoy". So Adults: Enjoy (orange) length: 8, Do not (blue): 2. Total adults: \(8 + 2 = 10\). Probability adults enjoy: \(\frac{8}{10}=0.8\). Children: Enjoy (blue) length: 8, Do not (orange): 2. Total children: \(8 + 2 = 10\)? No, that would make probability same. Wait, maybe I misread. Wait, the options are 4 times, 2.5, 3.75, 3.2. Wait, maybe the counts are: Adults: Enjoy (orange) is 2, Do not (blue) is 8? No, the orange bar for adults is longer. Wait, let's look at the number of segments at the top (the small icons). There are 10 icons (from the top: 10 small figures). So Adults: Enjoy (orange) has 8 figures, Do not (blue) has 2. Children: Enjoy (blue) has 8 figures, Do not (orange) has 2? No, that's same. Wait, no, maybe the "Enjoy" for children is 8, "Do not" is 2, and for adults "Enjoy" is 2, "Do not" is 8. Wait, the blue for adults is "Do not Enjoy", orange is "Enjoy". So adults: Do not (blue) is 2, Enjoy (orange) is 8. Children: Enjoy (blue) is 8, Do not (orange) is 2. So probability adults enjoy: \( \frac{8}{10} = 0.8\). Probability children enjoy: \( \frac{8}{10}=0.8\)? No, that can't be. Wait, maybe the total number of people: Adults: Enjoy (orange) = 8, Do not (blue) = 2 (total 10). Children: Enjoy (blue) = 8, Do not (orange) = 2 (total 10). No, that's same. Wait, maybe the graph is different. Wait, the options are 4 times more likely. Wait, maybe adults: Enjoy (orange) is 2, Do not (blue) is 8 (total 10). Probability adults enjoy: \( \frac{2}{10}=0.2\). Children: Enjoy (blue) is 8, Do not (orange) is 2 (total 10). Probability children enjoy: \( \frac{8}{10}=0.8\). Then the ratio is \( \frac{0.8}{0.2}=4\). Ah, that makes sense. So I misread the colors. Adults: "Do not Enjoy" (blue) is 8, "Enjoy" (orange) is 2. Children: "Enjoy" (blue) is 8, "Do not Enjoy" (orange) is 2. So total adults: \(8 + 2 = 10\), probability adults enjoy: \( \frac{2}{10}=0.2\). Total children: \(8 + 2 = 10\), probability children enjoy: \( \frac{8}{10}=0.8\). Then the number of times more likely: \( \frac{0.8}{0.2}=4\).

Step2: Calculate the ratio

Probability children enjoy: \(P_{c}=\frac{\text{children enjoy}}{\text{total children}}=\frac{8}{10} = 0.8\). Probability adults enjoy: \(P_{a}=\frac{\text{adults enjoy}}{\text{total adults}}=\frac{2}{10}=0.2\). Ratio: \(\frac{P_{c}}{P_{a}}=\frac{0.8}{0.2}=4\).

Answer:

4 times more likely