# Probability: Considering Failure Rates

The records of Midwestern University show that in one semester, 38% of the students failed mathematics, 27% of the students failed physics, and 9% of the students failed mathematics and physics. A student is selected at random.

a.) If a student failed physics, what is the probability that he or she failed mathematics?

b.) If a student failed mathematics, what is the probability that he or she failed physics?

c.) What is the probability that he or she fails mathematics or physics?

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#### Solution Preview

a) Let's put numbers first to make things clear. Suppose the number of students is 100. Then among these students, 27 failed physics, and 9 failed both: physics and mathematics. The important fact here is that these 9 that failed both are among the former 27. Hence if we pick at random a student who failed physics (i.e. between 27 students), the probability ...

#### Solution Summary

This solution provides detailed reasoning to explain how to formulate the necessary ratios required to solve for these probability-based questions. All final answers are given as ratios and this solution is just under 270 words.