Name: Mark Haberman
Who is asking: Other
Level: All

Question:
Last semester, the grade distribution in a quantitative methods course had the following distribution: 10% A, 25% B, 35% C, 10% D, and 15% W (withdrew).

1. If this grade distribution does not change this semester, what is the probability that a randomly selected student will make at least a D?
2. If this grade distribution does not change this semester, what is the probability that a randomly selected student will fail the course?
3. If this grade distribution does not change this semester, what is the probability that a randomly selected student who finished that course (did not withdraw) made a grade of D or better?

I assume that the missing 5% failed the course last semester.

1. Last semester the percentage who made a D at least was 10% + 25 + 35% + 10% = 80%. Hence, if the distribution does not change, 80% of the students this semester will get at least a D. That is the probability that a randomly selected student will receive at least a D is 0.8.
2. Similar to 1.
3. If the number of students who take the course this semester is N and the distribution does not change then the number of students who finish the class will be 0.85N, that is 85% of them. Then number who will receive a D or better is 0.8N and thus the probability that a randomly selected student who finishes that course (did not withdraw) mades a grade of D or better is 0.8N/0.85N = 0.8/0.85 = 0.94