Let A be the event that a student is enrolled in an accounting course, and let S be the event that a student is enrolled in a statistics course. It is known that 30% of all students are enrolled in an accounting course and 40% of all students are enrolled in statistics. Included in these numbers are 15% who are enrolled in both statistics and accounting.
a. Find P(S).
b. Find the probability that a student is in accounting and is also in statistics.
c. A student is randomly selected, and it is found that the student is enrolled in accounting. What is the probability that this student is also enrolled in statistics?
d. A student is randomly selected, and it is found that the student is enrolled in statistics. What is the probability that this student is also enrolled in accounting?
e. A student is randomly selected, what is the probability that the student is enrolled in either accounting or statistics or both?
f. From this information, what can be concluded about two events?