Page of3 O ZOOM + 7) In a group of 100 students, a total of 40 students take Math, a total of 20 students take History, and 10 students take both Math and History. Let M : student is taking Math, H : student is taking History 3) Fill in the counts in each section ofthe contingency table below. (2 pts) a) Find probability that a randomly selected student is... Express using probability notation. (1 pt each) i) Taking Math or History ii) Not taking Math iii) Taking neither Math nor History iv) Taking History, given he/she is taking Math v) Taking History, given he/she is not taking Math vi) Taking Math, given he/she is taking History b) Are the events M and H mutually exclusive? Use probability tojustify. (2 pts) e) Are the events M and H independent? Use probabilities to justify. (4 pts)