Math probability

Question

the probability that a student is in honors given that he or she is in mrs rollins class is 28/51. the probability that a student is not in ms rollins class given that he or she is not in honors is 33/56 if there are 165 students that are neither in mrs rollins class nor in honors how many are in mrs rollins class and in honors

Answer 1

We have 165 students that are neither in Rollins' class nor in honors

 

33/56 of the nonhonors students is 165

Let N = # nonhonor students

(33/56)N = 165

N = 165(56)/33 = 280 total nonhonors students

 

Since there are 280 total nonhonors students and

165 of then are not in Rollins' class... Then

280-165 = 115 nonhonors students ARE in Rollins' class

 

Then 23/51 of Rollins students = 115

Let R = # students in Rollins class

(23/51)R = 115

R = 115(51)/23 = 255 total students in Rollins' class

 

Of that 255 we have 115 that are not in honors

leaving 140 honors students in Rollins class