- Wed Mar 02, 2022 6:04 pm
#94021
Hi Christmas,
You are correct, this is absolutely an issue with numbers and percentages. Specifically, the problem is that the conclusion looks at a percentage (likelihood of a collision), but we are missing the denominator in the fraction.
To break this down, let's uncover the hidden math problem. The conclusion says that if you bicycle on the left you are more likely to get into a collision than if you bicycle on the right side. How do you calculate the likelihood you will get in a collision if you ride on the left side? Well, you want to take the number of collisions with bicyclists on the left half of the road and divide that by the total number of bicycle trips on the right side of the road. You would then do that same calculation for people who rode on the right hand side and compare the two percentages.
Let's plug in some simple numbers to make this clearer. Technically we want to look at the bicycle trips taken, not the number of people (who may have taken multiple trips), but I'm going to simply it and imagine that each person only took one trip. Say 200 people went for a bike ride yesterday, 100 of them rode on the left side of the road and 100 of them rode on the right side of the road. 20 people on the left side got into an accident, but only 5 people on the right side did. That would mean that the left-siders had a 20% chance of getting into an accident, but the right-siders only had a 5% chance of getting into an accident. Conclusion: left side is more dangerous.
However, it may not be an even split. What if 1,000 people rode on the left side and 100 people rode on the right side, and we had the same number of collisions respectively? Well, now the left-siders had a 2% chance of collision, and the right siders still had a 5% chance of collision. Same number of accidents, but by changing the total, the likelihood changed too. Now the right side is more dangerous.
Answer choice (B) addresses this problem. The bicycle safety expert's argument doesn't make any sense unless we know how much of the bicycling took place on the left side vs. the right side.
This exact problem comes up over and over and over again on these questions. To calculate a percentage you need to know both the numerator (how many bicycle accidents there were) and the denominator (how many total bicycling trips took place). This problem is a little trickier because you have two percentages to calculate, the likelihood of collision on the left side and on the right side, and then you have to compare the two. But the basic principle is the same.
Hope that helps!
Beth
