Chapter 10.2, Problem 5E

Solution

To find: The counts in the table.

The required values are:

  $\begin{array}{cc}\left(a\right)42& \left(b\right)6\\ \left(c\right)168& \left(d\right)24\end{array}$

Given information:

An engineer designing a new electronic device needs to be sure that both left-and right-handed people can operate it successfully. She’ll have a test group try it out, and she plans to summarize the results in a table like the one shown in the table:

  $\begin{array}{cccc}& \text{Successful}& \text{Failed}& \text{Total}\\ \text{Lefty}& \left(a\right)& \left(b\right)& 48\\ \text{Righty}& \left(c\right)& \left(d\right)& 192\\ \text{Total}& \text{210}& 30& 240\end{array}$

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 top 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,

  $\begin{array}{c}\left(a\right)=\frac{48\times 210}{240}\\ =\frac{10,080}{240}\\ =42\\ \left(b\right)=\frac{48\times 30}{240}\\ =\frac{1440}{240}\\ =6\\ \left(c\right)=\frac{192\times 210}{240}\\ =\frac{40,320}{240}\\ =168\\ \left(d\right)=\frac{192\times 30}{240}\\ =\frac{5760}{240}\\ =24\end{array}$

Conclusion:

The required values are:

  $\begin{array}{cc}\left(a\right)42& \left(b\right)6\\ \left(c\right)168& \left(d\right)24\end{array}$