Please show your work and explain how you got to the answer, thank you.

The student information survey data represents 91 students from this ST 201 class. Among all 91 students surveyed: I 28 students say they prefer math over writing 0 85 students reported that the United States is their home country I 26 students say they prefer math AND consider the United States their home country Please show your work. a) (1 point) Given a student that considers the US their home country is selected, what is the chance they prefer math? P(prefer math | US is home country) = b) (1 point) Given a student that prefers math is chosen, what is the probability they consider the US their home country? P(US is home country I prefer math) = c} (1 point) Among students in our class, is the event \"prefer math\" independent from \"US is home country\"? Explain. Show mathematical reasoning. Part III. (7 points) In the student information survey, you were each asked the following question: Which area ofstudy is majorfocused (pick only one}?The table below shows the distribution of answers to this question. 10 0 8 12 35 23 3 a) (3.5 points) Fill in the probability of randomly selecting a student from each ofthe majors. Round to 3 decimal places. b) (1.5 points) Check your probability model. Explain reasoning or show work for each check. I Are the evens assumed to be disjoint/mutually exclusive? / ls each probability between 0 and 1? J Do all the probabilities add to 1? (Is okay if it is just slightly off due to rounding) c) (1 point) If we choose one student at random, which major is the most likely to be selected? d) (1 point) What is the chance you select a student with a major in either Business or Psychology? P(Business or Psychology) =