Question

At Litchfield College of Nursing, 81% of incoming freshmen nursing students are female and 19% 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

Incomplete question. Here is the other missing part of the question.

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

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

ii) These probabilities are the same.

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

Conditional Probability:

The conditional probabilities for two independent event A and B are

P(A|B) = P(A)

and

P(B|A) = P(B).

However, when A and b are not independent, then the conditional probability, that is the probability of A given B is calculated as:

P(A|B) = P(A∩B)/P(B)

***Answer and Explanation:

Given Information:

Let M and F denote the event that a randomly selected student is a male or a female respectively, and P denote the event that a given student graduates.

P(F)=0.84

P(M)=0.16

P(P|F)=0.70

P(P|M) =0.80

(a)

The probability that a randomly selected student will graduate given that the student is a female is:

P(student will graduate istudentisfee)

= P(P|F) = 0.70

(b)

The probability that a randomly selected student will graduate and the student is a female is:

P(student will graduate and student is male) = P(P∩F)=P(P|F)×P(F) =0.70×0.84=0.588

(c)

The probability that a randomly selected student will graduate given that the student is a male is:

P(student will graduate |s student is male) = P(P|M) = 0.80

(d)

The probability that a randomly selected student will graduate and the student is a male is:

P(student will graduate and student is male) = P(P∩M) = P(P|M)×P(M) = 0.80×0.16=0.128

(e)

The probability that a ranndomly selected student will graduate is:

P(student will graduate)=P(student will graduate and student is female)+P(student will graduate and student is male)=

P(P∩F)+P(P∩M) = 0.588+0.128=0.716

(f)

Option (iv) is the correct answer. the term 'and' refers to the sample space of all students, while the term 'given' refers to restricting the sample space to females only.