Question

At Litchfield College of Nursing, 83% of incoming freshmen nursing students are female and 17% are male. Recent records indicate that 70% of the entering female students will graduate with a BSN degree, while 80% of the male students will obtain a BSN degree. If an incoming freshman nursing student is selected at random, find the following probabilities. (Enter your answers to three decimal places.) (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 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?

Answer 1

Graduate No Gradeuate Female Male Totals 0.595 0.12 0.715 B1 0.255 0.03 0.285 B2 0.85 A1 0.15 A2 a) P( Student graduatelfemale) P( graduate & Female)/P( Female) 0.595/0.85 0.7 b) P( Student is gradeuate & Female) 0.595 c) P( Student graddeuatel Male) P( Graduate & Male) /P( Male) 0.12/0.15 0.80 d) P( Gradeuate & Male) 0.12 e) P( Student graduate) 0.715

Answer 2

Let F = event student is female, M=event student is male, G = event student will graduate, and N = event student does not graduate.

1. P(G given F) = 0.70                     
2. P(F and G) = P(F)×P(G given F) = 0.83x0.7 = 0.581
3. P(G given M) = 0.80
4. P(G and M) = P(M)×P(G given M) = 0.17x0.80 = 0.136
5. P(G) = P(G given F) + P(G given M)    (since a grad is either male or female)

   = 0.581 + 0.136 = 0.717

1. P(G or F) = P(G) + P(F) – P(G and F)

           = 0.717 + 0.83 – 0.581 = 0.966