Question

At Litchfield College of Nursing, 87% of incoming freshmen nursing students are female and 13% are male. Recent records indicate that 60% 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 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?

The term and refers to the sample space of all students, while the term given refers to restricting the sample space to females only.

These probabilities are the same.    

This is by chance. These probabilities are typically the same.

The term given refers to the sample space of all students, while the term and refers to restricting the sample space to females only.

Answer 1

(a) 70% since you are told that is how many of the female students graduate.

(b) Using the conditional probability formula: P(A | B) = P(A and B) / P(B), we multiply by P(B) to get that P(A and B) = P(A|B)*P(B). So, if A = Graduate and B = Female, we need to find P(Grad | Female)*P(Female) = 70%*82% = 57.4%!

a. P(student will graduate | students is female) = 0.85
-----------------------------
b. P(student will graduate AND student is female)
= P(female)*P(grad|female) = 0.35*0.85
--------------------------------------------
c. P(student will graduate) = 0.8*0.65+0.85*0.35

-------------------------------------------------------
d. If you answers in part �a� and �b� are the same, explain why. If they are different, explain why.
I'll leave that to you.