### Brain Teasers

# Slow and Stupid Wins the Race?

Hare and Tortoise had to take a make-up class in math over the summer, a two-month, self-paced course with a test at the end of each of 12 chapters. The course requires a 70% grade to pass.

In the first month, they both had difficulties with the concepts. Hare averaged 60% on his exams; Tortoise averaged 50%. Owl, the supervisor, spent three days of the next week helping them with their difficulties.

It worked. In the second month, Hare averaged 90% on his exams; Tortoise averaged 80%.

However, Tortoise got a passing grade of 75% in the class; Hare failed with 65%. When Hare protested to Owl that he'd outscored Tortoise in both months, Owl made Hare do the math on the board -- and sign up for another make-up class, after school in the fall.

How did Tortoise pass while Hare flunked?

In the first month, they both had difficulties with the concepts. Hare averaged 60% on his exams; Tortoise averaged 50%. Owl, the supervisor, spent three days of the next week helping them with their difficulties.

It worked. In the second month, Hare averaged 90% on his exams; Tortoise averaged 80%.

However, Tortoise got a passing grade of 75% in the class; Hare failed with 65%. When Hare protested to Owl that he'd outscored Tortoise in both months, Owl made Hare do the math on the board -- and sign up for another make-up class, after school in the fall.

How did Tortoise pass while Hare flunked?

### Hint

They worked at different speeds.### Answer

In the first month, Hare took 10 chapter tests; Tortoise took only 2. In the second month, Hare took his remaining 2 exams and Tortoise took the 10 he needed to finish.Hare's average = (10*60 + 2*90) / 12 = 780/12 = 65

Tortoise's average = (2*50 + 10*80)/12 = 900/12 = 75

Mathematicians know this as Simpson's paradox.

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