In a class of 30 students, 19 study Physics, 17 study Chemistry, and 15 study both of these subjects.
(1) Display this information on a Venn diagram.
(2) Hence determine the probability that a randomly selected student from this class studies: both subjects
(3) Hence determine the probability that a randomly selected student from this class studies: at least one of the subjects
(4) Hence determine the probability that a randomly selected student from this class studies: Physics but not Chemistry
(5) Hence determine the probability that a randomly selected student from this class studies: exactly one of the subjects
(6) Hence determine the probability that a randomly selected student from this class studies: neither subject.