Directions: Show all your work. Indicate the methods you use, because you will be graded on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. Problem: Suppose a college professor has 30 students in her class. There are 22 females and 8 males. At the start of class on the professor routinely goes over the homework from the previous class. Unbeknownst to the professor, only 4 of the males and 8 of the females have completed the homework assignment. The professor chooses students at random to explain homework problems. (a) What is the probability that a randomly selected student has in fact completed the homework assignment? (b) Are the events \"choosing a female\" and \"choosing a student who completed the homework\" independent of each other? Justify your answer. The professor randomly selects 5 students to explain homework problems. (cl Describe how to use a table of random digits to estimate the probability that 2 or fewer of the 5 randomly selected students completed the assignment. (d) Complete three repetitions of your simulation starting with line 102 in the table of random digits below and use the results to estimate the probability described in part (c). TABLE B Random digits LINE 10l 19223 95034 05756 28713 96409 [2531 42544 82853 102 73676 47150 99400 01927 27754 42648 82425 36290 103 45467 71709 77558 [11095 32863 29185 82226 90056 104 52711 38889 93074 60227 40011 85848 48767 52573 105 95592 941507 69971 914-51 60779 53791 17297 59335 106 68417 35013 15529 72765 85089 57067 50211 47437 107 82739 57890 20807 17511 81676 55300 94383 14893