A university conducted a study into students’ perceived usability of a proposed upgrade to the existing learning management system (LMS). Students were asked to visit a test site and evaluate the proposed LMS relative to their perceptions of the existing LMS. To further evaluate the results, participants were asked to nominate one field that represented their primary area of study. Some 84% of students perceived the proposed LMS to be superior in usability to the existing system. Of the students sampled, 45% were primarily studying business and rated the proposed system to be superior in usability. Of those students primarily studying science, 95% found the proposed LMS easier to use; these students represented 30% of the surveyed participants. Together, those students primarily studying science and those primarily studying business made up 85% of the sample. If a student is selected randomly, determine the probabilities of the following.

(a) The student rates the proposed system as superior in usability given that the student primarily studies business.

(b) The student rates the proposed system as superior in usability given that the student primarily studies in an area other than business.

(c) The student is studying science, given they do not believe the proposed system to be superior in usability.

(d) The student is primarily studying science and believes the proposed system to be superior in usability.