Chapter 10.2, Problem 6E

Solution

To solve: The counts in the table.

The required values are:

  $\begin{array}{cc}\left(a\right)77& \left(b\right)143\\ \left(c\right)84& \left(d\right)156\\ \left(e\right)49& \left(f\right)91\end{array}$

Given information:

A pollster plans to survey a group of voters, asking them whether they favor or oppose the death penalty, and will summarize the responses in a table like the one shown in the table:

  $\begin{array}{cccc}& \text{Favor}& \text{Oppose}& \text{Total}\\ \text{Republican}& \left(a\right)& \left(b\right)& 220\\ \text{Democrat}& \left(c\right)& \left(d\right)& 240\\ \text{Other}& \left(e\right)& \left(f\right)& 140\\ \text{Total}& 210& 390& 600\end{array}$

Concept used:

Two events are independent, if the probability that one event occurs in no way affects the probability of the other event occurring.

When the ability to operate the device is independent of handedness, then the counts in the table are obtained by multiplying the correspond row total and corresponding column total divided by the table total.

Calculation:

Then,

  $\begin{array}{c}\left(a\right)=\frac{220\times 210}{600}\\ =\frac{46,200}{600}\\ =77\\ \left(b\right)=\frac{220\times 390}{600}\\ =\frac{85,800}{600}\\ =143\\ \left(c\right)=\frac{240\times 210}{600}\\ =\frac{50,400}{600}\\ =84\\ \left(d\right)=\frac{220\times 390}{600}\\ =\frac{93,600}{600}\\ =156\\ \left(e\right)=\frac{140\times 210}{600}\\ =\frac{29,400}{600}\\ =49\\ \left(f\right)=\frac{140\times 390}{600}\\ =\frac{54,600}{600}\\ =91\end{array}$

Conclusion:

The required values are:

  $\begin{array}{cc}\left(a\right)77& \left(b\right)143\\ \left(c\right)84& \left(d\right)156\\ \left(e\right)49& \left(f\right)91\end{array}$