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.

(c) 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).

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