“A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?”

According to the study below, around 5% to 40% of respondents gave the answer “5 cents”, varying from one survey to another. Asking for both the price of the bat and the ball did not improve the accuracy. When further asked if their answers differed by $1, 86% of those who said the bat was $1 and the ball was 10 cents claimed that their answers differed by $1.

When forced to choose between either 5 cents or 10 cents, the percentage correct increased from 10% to 19%.

Returning to the original problem, giving a massive bold warning to check one’s answer carefully did not significantly change the correct response rate. When instead being told specifically “Hint: 10 cents is not the answer”, the percentage correct surged from 38% to 67%, with the percentage answering 10 cents dropping from 54% to 20%.

Being specifically instructed to consider that the answer might be 5 cents increased the percentage correct from 12% to 32%. (Although, 8% of participants chose 33 cents when asked to consider if the answer is 33 cents.) https://law.yale.edu/system/files/area/workshop/leo/document/Frederick_Bat-BallProblem.pdf

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