Question

In a nursing program, 85% of incoming freshmen nursing students are female while 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.

Suppose an incoming freshman nursing student is chosen at random. Use a tree diagram or probability formula to find the following.

a. Find the probability the student is female and graduates with a BSN degree.

b. Find the probability the student graduates with a BSN degree.

c. Find the probability the student is a female given that the student graduates with a BSN degree.

Answer 1

Probability that incoming freshmen nursing students are female = 0.85

Probability that incoming freshmen nursing students are male = 0.15

Probability that entering female students will graduate with a BSN degree = 0.70

Probability that entering male students will graduate with a BSN degree = 0.90

a)

Probability the student is female and graduates with a BSN degree

= Probability the student is female * Probability that entering female students will graduate with a BSN degree

= 0.85 * 0.70

= 0.595

Probability the student is female and graduates with a BSN degree is 0.595

b)

Probability the student graduates with a BSN degree

= Probability that entering female students will graduate with a BSN degree OR Probability that entering male students will graduate with a BSN degree

=(0.85 * 0.7) + (0.15*0.9)

= 0.595 + 0.135

= 0.73

Probability the student graduates with a BSN degree is 0.63

c)

Probability the student is a female given that the student graduates with a BSN degree

= P(student is a female | student graduates with a BSN degree)

= P(student is female and graduates with a BSN degree) / P(student graduates with a BSN degree)

= (0.85*0.7) / 0.63

= 0.595 / 0.63

= 0.94 (Round to 2 decimal)

Probability the student is a female given that the student graduates with a BSN degree is 0.94