Question

At Litchfield College of Nursing, 85% of incoming freshmen nursing students are female and 15% are male. Recent records indicate that 60% 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.)

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

Let F = event student is female, M=event student is male, G = event student will

graduate, and N = event student does not graduate.

(a)

P(GgivenF) = 0.60

(b)

P(FandG) =P(F)·P(GgivenF) = (0.85)(0.6) = 0.51

(c)

P(GgivenM) = 0.80

(d)

P(GandM) =P(M)·P(GgivenM) = (0.15)(0.80) = 0.12

(e)

P(G) =P(GgivenF) +P(GgivenM) = 0.51 + 0.12 = 0.63 (since a grad is either male orfemale)

(f)

P(GorF) =P(G) +P(F)−P(GandF) = 0.63 + 0.85−0.51 = 0.97

in first sentence sample will consist of bith male and female but in second case we have to select from the sample of females only