Suppose we have the following facts of students in a large class: 35% of them like math; 59% of them like English; 80% of them like English or history; 11% of them like math and English; 8% of them like math and history; 10% of them like English and history; 2% of them like math, English and history. Let M, E and H denote the events that a randomly selected student from this class likes math, English and history respectively. (a) What is the probability a selected student likes just one of the subjects? (b) What is the probability that a student likes none of the three subjects? (c) Is a student liking math independent of a student liking history? Justify your answer mathematically. (d) If a random sample 3 students are chosen, what is the probability that exactly 2 of them like math