Answer to Question #131906 in Statistics and Probability for Lawrence Okyne

Question

Imagine a secondary school which has 100 students in it's 12 grade class 50 students studies mathematics 29 studies biology 13 study both subjects.
What is the probability that the students studies biology but not math

Answer 1

Let S represents Universal set of secondary school population.

Let M represents the subset of students taking Mathematics in class.

Let B represents the subset of students taking Biology in class.

Therefore:   S=100

                      M=50                 

                    B=29

                     M/B= 13 ,where M/B is intersection of sets.

Therefore, those taking only:

                  Mathematics = M- MB

                   =50-13=37

                  Biology =B- M/B

                    =29-13=16

Those who take neither Mathematics nor    Biology are:

                  =Y-[ M- M/B]+[ B- M/B]

             100-37-16=100-(37+16+13) =34

Therefore, chance of student that studies mathematics but not biology is

     16/100=0.16