On a certain online math assignment, a student is allowed to submit an unlimited number of answers before moving on to the next problem. The problem is a free response question, and the student believes that his guessed answer is correct about 7% of the time. (There are so many possible guesses that he thinks this ratio stays the same every time.) Under these assumptions, let X be the number of times he needs to submit a different random guessed answer until he gets the question correct.
a. How many tries should he expect if he wants to get this question right without actually learning the material?
b. What is the probability it takes him at least 20 tries to get the question right?
c. If there are 10 homework questions of a similar nature on this assignment, and he uses the same random technique with all of the questions, what is the probability it takes him at least 20 tries to get each of these questions right? What distribution is being used here? What are the parameters?
d. If each homework question takes him 2 minutes to read (once) and 30 seconds for each random entry attempt, what is the expected time it will take him to get one question correct? What about the 10 question assignment? (Do you think he would have been better off just learning the material and doing the homework properly?)