A) The records of Midwestern University illustrate that inone semester, 38% of students failed mathematics, 27% of the students failed physics, and 9% of students failed mathematics and physics. The student is selected at random.
i. If the student failed physics, find probability that he or she failed mathematics?
ii. If the student failed mathematics, find probability that he or she failed physics?
iii. Find probability that he or she failed mathematics or physics.
B) In game Over and Under, pair of dice is rolled and one can bet on whether sum of dots showing on dice is over 7, under 7, or exactly 7. Find odds in favor of you winning when you bet that over 7 wins?
C) In 20 item true-false examination:
i. Find probability that the student will get all correct answers by chance if he or she is guessing?
ii. If 12 correct answers has passing grade, find probability that he or she will pass?
iii. Determine the odds in favor of passing?
D) If A1, A2, and A3 form the partition of the sample space S and if P(A1) = 0.2,P(A2) = 0.4, P(A3) = 0.4 and if E is event of S for which P(E A1) = 0.01, P(E A2) = 0.02, and P(E A3) = 0.01. Determine P(A1 E).