Question

At Litchfield College of Nursing, 87% of incoming freshmen nursing students are female and 13% 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 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. The term given refers to the sample space of all students, while the term and refers to restricting the sample space to females only.     These probabilities are the same. This is by chance. These probabilities are typically the same.

Answer 1

(a)

From the given data, the following Table calculated:

	Graduate	Not Graduate	Total
Female	0.87 X 0.70 = 0.609	0.87 - 0.609 = 0.261	0.87
Male	0.13 X 0.90 = 0.117	0.13 - 0.113 =0.013	0.13
Total	0.726	0.274	1.00

P(Graduate/ Female) = P(Graduate AND Female)/ P(Female)

                              = 0.609/0.87 = 0.7

So,

Answer is:

0.7

(b)

P(Graduate AND Female) = 0.609

(c)
P(Graduate/ Male) = P(Graduate AND Male)/ P(Male)

                          = 0.117/ 0.13 = 0.9

So,

Answer is:

0.9

(d)
P(Graduate AND Male) = 0.117

(e)

P(Graduate) = 0.726

(f)

The probabilities P(will graduate and is female) and P(will graduate /female)) are different because P(will graduate and is female) is a compound probability of the events "Will graduate" and "Female". P(will graduate /female) is the conditional probability of the event :Will graduate" given that it is"Female".

So,

Correct option:

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