Chapter 10.3, Problem 3E

To determine

To calculate:

The values from the incomplete two-way table:

		Preparation		Total
		Studied	Did Not Study
Grade	Pass		$6$
	Fail			$10$
Total		$38$		$50$

Answer to Problem 3E

The completed two-way table is as follows:

		Preparation		Total
		Studied	Did Not Study
Grade	Pass	$34$	$6$	$40$
	Fail	$4$	$6$	$10$
Total		$38$	$12$	$50$

Explanation of Solution

Given information:

A partial survey report is given about the preference of female students to take a gym class or choir.

		Preparation		Total
		Studied	Did Not Study
Grade	Pass		$6$
	Fail			$10$
Total		$38$		$50$

Calculation:

For completion of the given table, first number the columns and rows as follows:

		Preparation		Total
		Studied	Did Not Study
Grade	Pass	$\left(\text{1},\text{1}\right)$	$\left(\text{1},\text{2}\right)$	$(1,3)$
	Fail	$\left(\text{2},1\right)$	$\left(\text{2},\text{2}\right)$	$\left(\text{2},\text{3}\right)$
Total		$\left(\text{3},\text{1}\right)$	$(3,2)$	$(3,3)$

Now, let’s find the missing numbers i.e. $\left(\text{1},\text{1}\right)$ , $\left(\text{1},3\right)$ , $\left(\text{2},\text{1}\right)$ , $\left(\text{2},\text{2}\right)$ , $\left(\text{3},\text{2}\right)$ .

For, $\left(\text{1},\text{3}\right)$ :

  $\left(\text{1},\text{3}\right)=(3,3)-(2,3)$

Substitute the values,

  $\begin{array}{l}\left(\text{1},\text{3}\right)=50-10\\ \left(\text{1},\text{3}\right)=40\end{array}$

For, $\left(\text{1},\text{1}\right)$ :

  $\left(\text{1},\text{1}\right)=(1,3)-(1,2)$

Substitute the values,

  $\begin{array}{l}\left(\text{1},\text{1}\right)=40-6\\ \left(\text{1},\text{1}\right)=34\end{array}$

For, $\left(\text{2},\text{1}\right)$ :

  $\left(\text{2},\text{1}\right)=(3,1)-(1,1)$

Substitute the values,

  $\begin{array}{l}\left(\text{2},\text{1}\right)=38-34\\ \left(\text{2},\text{1}\right)=4\end{array}$

For, $\left(\text{2},\text{2}\right)$ :

  $\left(2,\text{2}\right)=(2,3)-(2,1)$

Substitute the values,

  $\begin{array}{l}\left(\text{2},\text{2}\right)=10-4\\ \left(\text{2},\text{2}\right)=6\end{array}$

For, $\left(\text{3},\text{2}\right)$ :

  $\left(\text{3},\text{2}\right)=(1,2)+(2,2)$

Substitute the values,

  $\begin{array}{l}\left(\text{3},\text{2}\right)=6+6\\ \left(\text{3},\text{2}\right)=12\end{array}$

Thus, putting the respected values in the table, the completed table is as follow:

		Preparation		Total
		Studied	Did Not Study
Grade	Pass	$34$	$6$	$40$
	Fail	$4$	$6$	$10$
Total		$38$	$12$	$50$