Chapter 15, Problem 12E

(a)

To determine

To find: the probability that the person is a student of the Arts and Sciences who is a 2^nd child or more if randomly selecting a student.

Answer to Problem 12E

0.103

Explanation of Solution

Given:

  

Calculation:

  $\begin{array}{c}P\left(A\cap S\right)=\frac{23}{223}\\ =0.103\end{array}$

There is a 10 percent chance that the selected student will be a second or more child of Arts and Science student.

(b)

To determine

To find: the probability that a student was among the students of the Arts and Sciences a 2^nd child or more.

Answer to Problem 12E

0.404

Explanation of Solution

Given:

  

Calculation:

Probability of students who are students of the arts and sciences, and second or more children

  $\begin{array}{l}P\left(S/A\right)=\frac{P\left(A\cap S\right)}{P\left(A\right)}\\ P\left(A\cap S\right)=\frac{23}{223}\\ P\left(A\right)=\frac{57}{223}\end{array}$

Put the value in the formula

  $\begin{array}{l}P\left(S/A\right)=\frac{P\left(A\cap S\right)}{P\left(A\right)}\\ =\frac{\frac{23}{223}}{\frac{57}{223}}\\ =0.404\end{array}$

There is a 40% probability that the student will be among students of Arts and Science and will be 2nd child or more.

(c)

To determine

To find: the probability that a student will be enrolled among 2^nd children or more in Arts and Sciences.

Answer to Problem 12E

0.2091

Explanation of Solution

Given:

  

Calculation:

  $P\left(A/S\right)=\frac{P\left(A\cap S\right)}{P\left(S\right)}$

Number of students who are students of the arts and sciences and second or more children is 23 $P\left(A\cap S\right)=\frac{23}{223}$

  $P\left(S\right)=\frac{110}{223}$

Put the value

  $\begin{array}{c}P\left(A/S\right)=\frac{\frac{23}{223}}{\frac{110}{223}}\\ =0.2091\end{array}$

There is a 21 percent chance that selected students are Arts and Science Students who are second or more children.

(d)

To determine

To find: the probability of enrolling a 1^st or only child in Agriculture College.

Answer to Problem 12E

0.0672

Explanation of Solution

Given:

  

Calculation:

Students in First Born and Human Ecology are 15

Therefore, the probability that the student is born first and that the student of Human Ecology is $\frac{15}{223}=0.0672$

Approximately 7 percent of students are both first-born and student of Ecology.

(e)

To determine

To find: the probability of an Agricultural student being a child, 1^st or only.

Answer to Problem 12E

0.233

Explanation of Solution

Given:

  

Calculation:

  $\frac{52}{223}=0.233$

There is a 23 percent probability that the chosen student will be the first child born to join the Agricultural College.