Prof. Lovell teaches two sections of MAT 301 this semester, with 30 students in the first section and 20 students in the second. After all, students submit Test 1, he randomly shuffles them before grading. Consider the first 15 test. a) What is the probability that exactly 11 of the test are from the second section? BOTH b) What is the probability that at least 11 of the test are from the second section? BOTH c) What is the probability that at most 4 of the test are from the second section? BOTH d) What is the probability that between 4 and 11 (inclusive) of the test are from the second section? e) What is the probability that exactly 6 of the test are from the same section? BOTH f) What are the mean and standard deviation of the number among these 15 test that are from the second section? BOTH

***Please show the steps in terms of R programming language, thank you.