Suppose we have the following facts of students in a large class 37% of them like math: 37% of them like English, 69% of them like English or history 10% of them like math and English; 11% of them like math and history: 9% of them like English and history 4% 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 6 students are chosen, what is the probability that exactly 3 of them like math?