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: o 28 students say they prefer math over writing a 85 students reported that the United States is their home country a 26 students say they prefer math AND consider the United States their home country a) {1 point) If we choose a student at random, what is the chance they prefer math over writing? P(prefer math) = b) {1 point) If we choose a student at random, what is the chance they consider the US their home country? P(US is home country): c) (1 point) If we choose a student at random, what is the chance they prefer math and consider the US their home country? P(prefer math AND US is home country) = d) {4 points) Using the information above, enter the correct proportions for each section of the Venn Diagram. If it is more convenient for you, write your work on a piece of paper, take a picture of it and paste it into your document. Prefer Math US is home country In a bookstore, the probability a customer buys a novel is 0.58 and the probability that the customer buys a non-fiction book is 0.31. Suppose the probability that the customer buys both a novel and a non- fiction book is 0.2. a) {1 point) Find the probability that the customer buys either a novel or a non-fiction book. Show your work. b) {1 point) What is the probability that a customer doesn't buy a non-fiction book nor a novel? Show your work. c) {1 point) Find the probability that a customer buys a novel given they are purchasing a non-fiction book. Show your work