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?
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 ...
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.