Fraction Brainteaser
Source: Sent to me by Gaurav Sinha Problem: Siddhant writes a Maths test and correctly answers 5 out of 6 Arithmetic questions and 20 out of 28 Geometry questions. In total, Siddhant scores 25 out of 34. Vaibhav writes another Maths test and correctly answers 20 out of 25 Arithmetic questions and 6 out of 9 Geometry questions. in total, Vaibhav scores 26 out of 34. Note that a) Vaibhav scores more than Siddhant b) Siddhant score better than Vaibhav in both individual topics - 5/6 > 20/25 and 20/28 > 6/9 How is it possible? Solution: Highlight the part between the * symbols for the answer. * This is Simpson's Paradox: each topic on its own shows one trend, but the combined score shows the opposite. Arithmetic is the easier topic - both students score a higher fraction there (Siddhant 5/6 = 83.3%, Vaibhav 20/25 = 80%) than in Geometry (Siddhant 20/28 = 71.4%, Vaibhav 6/9 = 66.7%). But the two tests mixed the topics very differently. Vaibhav's...