A class of 40 students has 10 honor students and 13 athletes

A class of 40 students has 10 honor students and 13 athletes. Three of the honor students are also athletes. One student is chosen at random. Find the probability that this student is an athlete if it is know that the student is not an honor student.

Solution

Dear Student Thank you for using Chegg !! Given a Class Total Number of Students (N) = 40 No Of Honor Students (H) = 10 No Of Athelete (A) = 13 No oF Honor and Athelete students (H & A) = 3 Only Athelete (A1) = A - (H&A) = 10 Only Honor = H - (H&A) = 7 Probability of student being an athelete given that he is not an honor student = Probability of student being only an athelete / Probability of student not being an honor student = P(C1) / P (D1) C1 = 10/40 D1 = (40-10)/40 = 30/40 Hence C1/D1 = 10/30 = 1/3