Conditional Probability

Question

In a second-semester English class, 40% of the students are sophomores and the rest freshmen; 25% of the sophomores are repeating the course and 15% of the freshmen gained admission to the course by advanced placement. The professor randomly selects a student to comment on the assignment. (Round your answers to three decimal places.)

(a) Find the probability that the professor selects a sophomore who is repeating the course.


(b) Find the probability that the professor selects a freshman who gained advanced placement admission to the class.

Answer 1

An easy way to solve this is to assume that there are 100 students in the class.  With this assumption there will be 40 sophomores and 60 freshmen.  25% or 1/4 of the sophomores are repeating the course, so the total number of repeat sophomores would be 40/4 = 10.  15% or 3/20 of the freshmen result from advanced placement, so (60)(3/20)=9 students fall into this category.  Now to answer the questions:

a)  probability of choosing a repeating sophomore will be 10/100 = 1/10 = 10%

b) probability of choosing an AP freshman is 9/100 = 9%