Classmates Ken and John have been comparing their past exam performances. On 60% of the exams, Ken received a grade of B or better. John received a grade of B or better on 70% of the exams. They noticed that on 90% of the exams on which Ken scored B or better, John also made B or better.
a. What proportion of the time did both Ken and John score B or better?
b. Suppose you choose one of the exams at random. How likely is it that at least one of the two failed to score B or better?
c. If you choose an exam at random and learn that John scored a B or better, how likely is it that Ken did not?
d. Are John’s test performance and Ken’s test performance statistically independent? Explain how you reached your conclusion.