Bayes Rule appears occasionally on MathCounts, and it helps to have clear notation. In this case **M** represents passing his math test and **–M** represents not passing math. Same for **S** and **–S** for passing and not passing the science test. **P(M|–S)** means the probability she passes math given she did not pass science.

I write out all the known data at the top, then use the formula for Bayes Rule to work through the computations. Finally, I take one more look at what the questions is asking and add together the appropriate probabilities.

(Source: MathCounts)

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## Published by mathproblemsolvingskills

I coach students preparing for MathCounts and the AMCs, and I teach using curricula published by Art of Problem Solving.
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