Grade Freshmen Sophomore Junior Senior A 0 8 9 10 B 0 6 8 11 C 1 7 9 12 D 2 4 1 4 F 0 6 2 1 TOTAL 3 31 29 38 What is the probability that the student is a junior and makes a B in the course? What is the probability that the student does not make a A in the course, given that the student is a senior? What is the probability that the student makes a 0 or F in the course? Let A be the event that a sophomore is taking the course. Let B be the event that the student makes a C in the course. Are the events A and B independent? Are the events A and B mutually exclusive? Grade Freshmen Sophomore Junior Senior A 0 8 9 10 B 0 6 8 11 C 1 7 9 12 D 2 4 1 4 F 0 6 2 1 TOTAL 3 31 29 38 Solution here total number of students=3+31+29+38=101 ##P[student is junior and scores B]=(total juniors who scores B)/total students=8/101=0.0079 [answer] ##P[a student does not make A in the course given that the student is senior]=P[a senior does not make A]/P[student is a senior]=((38-10)/101)/(38/101)=28/38=0.73684 [answer] ##P[a student makes F]=total students make F/total students=(0+6+2+1)/101=0.08910 [answer] ##A be the event that a sophomore is taking the course. B be the event that the student makes C in the course. so P[A]=31/101 P[B]=(1+7+9+12)/101=29/101 now P[AB]=P[a sopomore makes C]=7/101 which is not eual to P[A]*P[B] so they are not independent moreover P[AB] is not zero..so not mutually exclusive also..