Bayes’ Rule

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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