At Litch­eld College of Nursing, 85% of incoming freshmen nursing students are female and 15% are male. Recent records indicate that 70% of the entering female students will graduate with a BSN degree, while 90% of the male students will obtain a BSN degree. If an incoming freshman nursing student is selected at random, ­find

(a) P (student will graduate | student is female).

(b) P (student will graduate and student is female).

(c) P (student will graduate | student is male).

(d) P (student will graduate and student is male).

(e) P (student will graduate). Note that those who will graduate are either males who will graduate or females who will graduate.

(f) The events described by the phrases “will graduate and is female” and “will graduate, given female” seem to be describing the same students. Why are the probabilities P (will graduate and is female) and P (will graduate | female) different?