Chapter 15, Problem 26E

(a)

To determine

To Explain: that Agriculture and Human Ecology are enrolling disjoint.

Answer to Problem 26E

Independent

Explanation of Solution

Suppose events are

O = Student enrolled other course

F = Student is first or only

T = Student is second or more

Let the events are,

A = Student enrolled Agriculture

S = Student enrolled Arts & Sciences

H = Student enrolled Human Ecology

It doesn’t have students enrolled in both Agriculture and Human Ecology.

  $P\left(A\cap H\right)=0$

Therefore Agriculture and Human Ecology are independent.

(b)

To determine

To Explain: that Agriculture and Human Ecology are enrolling independent.

Answer to Problem 26E

Not independent

Explanation of Solution

Consider

  $\begin{array}{c}P\left(A\backslash H\right)=\frac{P\left(A\cap H\right)}{P\left(H\right)}\\ =\frac{0}{\frac{43}{223}}\\ =0\\ P\left(A\right)=\frac{93}{223}\\ P\left(A\backslash H\right)\ne P\left(A\right)\end{array}$

Therefore, they are not independent.

(c)

To determine

To Explain: firstborn and enrolling in Human Ecology are disjoint.

Answer to Problem 26E

Not disjoint

Explanation of Solution

We have

  $\begin{array}{c}P\left(F\cap H\right)=\frac{15}{223}\\ \ne 0\end{array}$

Therefore Human Ecology and being first born are not disjoint.

(d)

To determine

To Explain: that firstborn and enrolling in Human Ecology are independent.

Answer to Problem 26E

Not independent

Explanation of Solution

Consider

  $\begin{array}{c}P\left(F\backslash H\right)=\frac{P\left(F\cap H\right)}{P\left(H\right)}\\ =\frac{\frac{15}{223}}{\frac{43}{223}}\\ =\frac{15}{43}\\ P\left(F\right)=\frac{113}{223}\\ P\left(F\backslash H\right)\ne P\left(F\right)\end{array}$

Therefore being first born and enrolling on human ecology are not independent.